Early Christianity

Much of the important work about religious diffusion has the seminal work of Rodney Stark on the rise of Christianity as its touchstone. Stark (Reference Stark1996a) drew on network concepts to help account for Christianity’s growth during the early Roman Empire, asserting that, similar to most new religious movements (Lofland and Stark Reference Lofland and Stark1965; Stark and Bainbridge Reference Stark and Bainbridge1980), the early church probably gained most of its converts through social ties. Were such ties strong or weak? István Czachesz (Reference Czachesz and Czachesz2011) argues that because the Apostle Paul was constantly traveling, he would have been unable to form strong ties with members of the communities he visited. Denis Duling (Reference Duling2013) disagrees, arguing that strong ties were necessary because converting was risky. He also notes that Paul’s longer stays as an artisan might have facilitated forming strong ties. Of course, Paul was not the only Christian missionary, but his evangelism model was widely influential.

Stark also argues that because most early Christians were Jews, when the Church sent missionaries to the far reaches of the Roman Empire, it would have been natural for them to stay with the Jewish Diaspora (i.e., Jews dispersed throughout the Roman Empire). He believes that the “mission to the Jews” was far more successful than most historians grant (see, e.g., Ehrman Reference Ehrman2018), and shows that cities with significant Diasporan communities Christianized sooner than did others (Stark Reference Stark1996a: 138–40; 2006: 134–35, 240).

Stark also shows that if the early church grew at a rate of approximately 40 percent per decade, a rate similar to that of the Mormon Church (Stark Reference Stark1996b), by 300 CE, it would have grown to approximately 6.3 million members, which is close to some estimates (Bagnall Reference Bagnall1982). In an expansion of Stark’s analysis, Adam Schor (Reference Schor2009) compares several potential growth scenarios, illuminating how different assumptions lead to various outcomes. He concludes by proposing a scale-free network model of early Christian growth (Barabási et al. Reference Barabási, Albert and Jeong1999). Scale-free networks are driven by preferential attachment (Merton Reference Merton1968), where most actors have only a few ties, while a handful (hubs) have numerous. Schor argues that such hubs could have served as brokers in the network for spreading Christian beliefs and practices. Moreover, scale-free networks can be resilient to external shocks because the random removal of actors tends to have little effect on network structure because most actors have few ties (Barabási Reference Barabási2002). Schor believes this might help explain the early church’s apparent ability to weather various storms (e.g., plagues, persecution), suggesting that it probably experienced “periods of relative stability broken by moments of explosive growth” (Schor Reference Schor2009: 497).

Stark (Reference Stark1996a, 2006) also tested several hypotheses regarding why Christianity took root in some cities but not others. Recently, Jan Fousek and several collaborators (Fousek et al. Reference Fousek, Kaše, Mertel, Výtvarová and Chalupa2018), using a dataset with as many as 324 cities, more robust population estimates, and distances weighted by travel costs, reconsidered two of Stark’s hypotheses: Christian congregations appeared sooner in (1) larger cities and (2) cities closer to Jerusalem. They found support for both, although the effects were stronger in the first two centuries. Additionally, they estimated the effective distance between pairs of cities, which is “the effect that a randomly seeded [innovation] in a peripheral node of the network has a higher probability of being transmitted to a well-connected hub than vice versa” (Brockmann and Helbing Reference Brockmann and Helbing2013: 1339). From this, they computed the shortest effective paths (beginning from Jerusalem), which allowed them to map a network of “the expected … spreading process” (Fousek et al. Reference Fousek, Kaše, Mertel, Výtvarová and Chalupa2018: 6) and measure Jerusalem’s direct impact on Christianity’s spread to nearby towns and distant regional centers (large cities). Their analysis suggests that once Christianity arrived at large cities, its diffusion no longer relied on Jerusalem.

Rabbinic Judaism, Military Cults, and Worshippers of the Most-High God

Archeologist Anna Collar has used network methods to map the spread of Rabbinic Judaism and other religious movements in the first few centuries of the Roman Empire. For Rabbinic Judaism, she draws on a modified version of PPA to link sites containing “Hebrew, Jewish symbols, or make explicit reference to Israel” (Collar Reference Collar and Knappett2013a: 235; Reference Collar2013b: 205). Specifically, she links each site to Judaea plus one established connection, “except in later cases where there are three [sites] close by” (Collar Reference Collar2013b: 212). Although “this skews the maps towards having very long-distance links and makes Judaea a heavy centre,” she believes it creates a more realistic picture of the “rabbinic ‘mission’ to the Diaspora” (Collar Reference Collar and Knappett2013a: 235). Because it is unclear how, whether, and when communities declined, she assumed that “once a piece of epigraphic evidence is recorded, Jews continued to be present” (Collar Reference Collar2013b: 212).

Collar shows that network connectivity in the Diaspora was sparse in the first and second centuries, suggesting minimal interaction between it and Jerusalem. In the third century, however, she constructs an increasingly interconnected network, which she attributes to the changes that ensued after the Romans destroyed the Second Temple in 70 CE. She argues that before the temple’s destruction, Diaspora Jews did not advertise their culture and identity because the temple was the center of religious life. Afterward, the influence of the Sadducees, which was tied to the temple, waned, while that of the rabbis, which was not, waxed. The ensuing Rabbinic reforms ultimately led to the “widespread dissemination and adoption of explicitly Jewish names, symbols, and language” (Collar Reference Collar and Knappett2013a: 230) throughout the Diaspora. Although Collar believes that the weak ties were important (ibid.: 242), she argues “that the new religious authorities … used … strong-tie ‘familial’ connections … to transmit the religious and social discipline of rabbinic Judaism” (ibid.: 230). Undoubtedly, many had to be “reactivated” because they had laid dormant for years (Collar Reference Collar2013b: 180). Like Stark (Reference Stark1996a), she believes that early Christianity probably utilized the same network and met some success among Diasporan Jews.

Collar turns to standard PPA to explore the diffusion of two other religious movements. One, Jupiter Dolichenus, which took its name from the Near Eastern storm god of Doliche (Dülük), a small town in what is now southeast Turkey, spread rapidly across the empire from about 125 to 300 CE before disappearing. At some point, this god became associated with war and the military, and Collar traces both its spread and disappearance to the mobility of Roman officers and the networks they left in their wake, “across which innovation and information flowed” (Collar Reference Collar2013b: 114). Her reconstructed networks (ibid.: 124–37) suggest that the cult peaked in the first half of the third century, but because it never took hold among the masses when Rome’s military networks fell into disarray in the third century due to political and military upheaval, its popularity waned. And once a plague struck in the middle to the late third century, it “could not sustain [itself], although a few dedications between 253 and 300 testify to its limping on in certain places” (ibid.: 144).

The other cult she explores, Theos Hypsistos, was a movement influenced by, but separate from, Judaism (ibid.: 269). She argues that two factors drove some “God-fearers,” those who observed Jewish rites without formally converting, to join the Hypsistarians: (1) the spread of Rabbinic Judaism and its associated reforms, and (2) a tax (fiscus Judaicus) imposed by the Roman Empire on anyone practicing Judaism (i.e., not just ethnic Jews). Rabbinic reforms had an effect because, reflecting increased tension between Jews and Romans due to various Jewish revolts, for a time, they drew distinct boundaries between who was and was not considered a Jew. This probably pushed the God-fearers away from Judaism and toward Hypsistarianism, where they could still “express their beliefs” (ibid.: 244). The fiscus Judaicus, which the Romans initially imposed to offset the lost revenues that Jews paid Rome for the destroyed Temple’s upkeep, was extended in 96 CE to all who openly practiced Judaism. This created an economic incentive for God-fearers to join the Hypsistarians, especially those who found the tax burdensome. Collar (ibid.: 274–81) demonstrates that the Hypsistarian network became increasingly interconnected in the second and third centuries, probably reflecting the influx of God-fearers. However, it all but disappeared in the fourth when the fiscus Judaicus lapsed, and Rabbinic Judaism relaxed its distinctiveness. The Hypsistarians probably also lost members to Christianity, given its similarities with Judaism, as well as becoming the Roman Empire’s state religion.

The Protestant Reformation

In an influential paper, economists Sascha Becker and Ludger Woessmann (2009) pioneered the use of distance from Wittenberg as an instrumental variable predicting the long-run influence of Protestantism on development. A slew of subsequent papers explored why self-governing cities adopted the Reformation, finding a positive association between proximity to Wittenberg, the center of the emerging Lutheran movement, and Zurich, the center of the emerging Reformed movement (Becker et al. Reference Becker, Pfaff and Rubin2016).

Distance measures from Wittenberg and Zurich work because they presume spatial diffusion from places of inception but is there evidence to suggest which mechanisms were at work? Steve Pfaff and his collaborators have drawn on social networks to help account for the spread of the German Protestant Reformation. In one, Kim and Pfaff (Reference Kim and Pfaff2012) examined the effect that student social networks had on the likelihood that a town embraced the Reformation (i.e., by abolishing the mass). In it, they argue that the university towns of Wittenberg and Basel, the respective intellectual homes of the Lutheran and Zwinglian reformers, acted as “critical communities” (ibid.: 190) that exposed the outside world to the Reformation’s theology. They show that the greater the number of students a city “sent” to Wittenberg or Basel, the more likely it would embrace reform. They also show that the greater the number of students a city sent to the orthodox Catholic strongholds, Cologne and Louvain, the more likely it would reject reform. Notably, these effects hold even after controlling for each city’s distance from Wittenberg or Basel (whichever was closer) and Cologne or Louvain (whichever was closer).

Subsequently, Wurpts, Corcoran, and Pfaff (Reference Wurpts, Corcoran and Pfaff2018) examined the Reformation’s diffusion in what is now Northern Germany. Previous studies found that members of the medieval Hansa (Hanseatic League), a network of merchants and trading cities with extensive ties in northern Europe, found the Reformation especially appealing for reasons of economy and local autonomy. To explore the Reformation’s diffusion among the Hansa, Wurpts et al. derived a network of ties between 34 Hansa towns based on their shared participation in 29 Hansa Diets (governance assemblies) in the 25 years leading up to the Reformation (1492–1516). Armed with these data, they first consider several topographical network measures (e.g., density, centralization, average path length) and conclude that the network meets the criteria for complex contagion. It enabled the “spread of information through multiple channels in the early years of the Reformation,” as well as offering “multiple opportunities for support and reinforcement, particularly at the center of the network” (ibid.: 233). Turning to generalized measures of degree, closeness, and betweenness centrality (Opsahl et al. Reference Opsahl, Agneessens and Skvoretz2010) allows them to control for both the number and weights of ties between towns. They find that tie strength between towns, having more ties to other towns (degree), being closer to other towns (closeness), and being located in positions of brokerage (betweenness) increased the likelihood that a town adopted reform.

Diffusion studies often confine themselves to a single channel of diffusion and model a single mechanism. However, a collaborative paper by Pfaff, fellow sociologist Yuan Hsiao, and economists Sascha Becker and Jared Rubin (Becker et al. Reference Becker, Hsiao, Pfaff and Rubin2020) proposes that the diffusion of radical institutional innovations depends on multiple networks and multiple forms of influence. Radical innovations spread where ideological entrepreneurs launch campaigns to persuade others, and multiple local social exchange ties reinforce those efforts, seeding local clusters of adopters across the network.

Answering Young’s (Reference Young2009) challenge to contend between learning, influence, and social contagion as explanations for diffusion, they use historical data and social network analysis to explain the diffusion of the early Reformation (up through 1530). They reconstructed the “influence network” of a single, hyperinfluential historical figure—Martin Luther—and compared its effect to learning using the printing press and spatial contagion. They found that about one-third of the cities in their sample that formed a personal tie with Luther by 1522, as measured through his correspondence network, his visits, and his students, adopted the Reformation. To get at a meaningful measure of social distance between cities, they reconstructed the sixteenth-century trade-route network based on historical atlases. A regression analysis revealed that, net of trade route centrality, a host of structural and economic factors, and the volume of local printing activity, ties to Luther increased the odds of adopting Protestantism.

Nevertheless, Becker et al. (Reference Becker, Hsiao, Pfaff and Rubin2020) acknowledge that multiple sources of endogeneity complicate a causal interpretation of the Luther effect. In response, they used computer simulations to pose counterfactual worlds in which only Luther’s influence operated, only spatial diffusion through trade networks from the Reformation’s point of inception at Wittenberg operated, and a world in which both factors combined to influence adoption. Based on simulation statistics drawn from their regression analyses and the historical record of adoption, agent-based modeling showed that a conservative scenario congruent with their theoretical model that combines Luther’s personal infectiousness and spatial contagion yields a rate of adoption close to the empirical observation.

Women’s Ordination

To study the spread of women’s ordination in American denominational Protestantism that has expanded rapidly since 1970, Mark Chaves (Reference Chaves1996, Reference Chaves1997) drew on the insights of the new institutionalism (DiMaggio and Powell Reference DiMaggio and Powell1983; Meyer and Rowan Reference Meyer and Rowan1977; Powell and DiMaggio Reference Powell and DiMaggio1991). The theory proposes that diffusion occurs through social exchange, positing that the more institutions interact, the more alike they become. To test whether this accounts for the spread of women’s ordination, Chaves estimated a series of event-history (survival) models that include several factors that could affect the likelihood that denominations would begin ordaining women. He included clergy shortages; theological beliefs; whether the denominations are predominantly rural, black, or Southern; founding dates; denominational structures (e.g., decentralized or autonomous women’s mission societies); feminism’s first (1880–1920) and second (1966–83) waves; and most importantly, ties to prior adopters in his models. Chaves first identified all the denominations that in 1992 had clergy, some degree of national-level organization, and more than 300 congregations. Because many of these resulted from mergers, he traced their development to determine all precursors. In the end, he identified 92 denominations, of which 44 ordained women. For network data, he constructed a series of (whole) networks where two denominations shared a tie if they belonged to one or more of the same ecumenical organizations at eight points in time between 1915 and 1985.

Chaves found that clergy shortages were not associated with adopting the innovation, but denominations that were younger, decentralized, or had autonomous women’s organizations were more prone to adopt. By contrast, denominations that were sacramental, predominantly Southern, and held the Bible was inerrant were less likely. Curiously, feminism’s second, but not first, wave increased the likelihood a denomination would begin ordaining women. The largest association Chaves uncovered, however, were ties to prior adopters. He found a positive relationship between the proportion of a denomination’s interorganizational ties to prior adopters and the likelihood it would begin ordaining women. Although his original analysis did not control for the effect that the more egalitarian Holiness and Pentecostal traditions may have had on the adoption of women’s ordination, a later analysis (Everton Reference Everton2018) using the same data did. It found that although the Holiness (but not the Pentecostal) tradition had a positive effect, the network effect remained, and its size was virtually identical.

The Spread of Islam in the United States

Erin Şakin (Reference Şakin2016) explored the diffusion of Islam in the United States. Collecting preconversion ego-network data for 30 recent Islamic converts, 18 in Michigan and 12 in Kentucky, he showed that in Michigan, which had an established Muslim community, individuals generally converted through weak ties, while in Kentucky, which did not, they generally converted through strong ties. Why? Şakin argues that because many Americans hold a negative perception of Islam, in areas where Muslims are more numerous (and thus more visible), non-Muslims are more likely to form weak ties with Muslims. By contrast, in areas with few Muslims, ties formed between non-Muslims and Muslims are more likely to be strong.

Repertoires and Cycles of Collective Action

Charles Tilly, Sidney Tarrow, and their many students and collaborators introduced an influential set of ideas about the spread of social movements (see, e.g., Traugott Reference Traugott1995). Based on an extensive program on the transformation of popular protest in Europe in the eighteenth and nineteenth centuries, Tilly (Reference Tilly1978) argued that people carry out a limited “repertoire” of collective action routines. These depend on their situation and exposure to different protest tactics, noting that national, modular, and autonomous forms of protest gradually replaced parochial and particular forms that relied on elite patronage. The gradual spread of the strike as the predominant form of labor protest exemplified this transition (ibid.: 151–66).

The notion of repertoires allowed Tilly to account for both the strong undercurrent of continuity, as well as the sweeping changes he documented in the comparative history of social movements. However, Tilly’s argument lacked a clear account of the origination and spread of novel protest forms. Why, for example, did new tactical forms seem to spread more rapidly in certain periods and jump across societies with different levels of economic development and urbanization? If we consider great waves of protest, such as those unleashed in 1848, 1968, 1989, or 2010, it seems that new forms of collective action spread rapidly both within and across societies, even when local conditions were unfavorable for their adoption and fostered strategic blunders (Hale Reference Hale2013; Weyland Reference Weyland2012). To better account for these periods, Tarrow (Reference Tarrow1994) developed the concept “cycles of contention,” which are conflict periods that feature the geographic and sectoral diffusion of protest. Of course, several factors could account for why diffusion occurs across cycles, among them heterogeneity, learning, and social influence. Indeed, Tarrow’s (1989) magisterial study of the great Italian protest wave of the 1960s and 1970s suggests that all three were at work. McAdam (Reference McAdam and Traugott1995) proposed a modification to this perspective in which “initiator” groups introduce innovations that other social movement organizations adopt as political opportunities expand.

Although the literature on protest repertoires originally focused on political opportunities and did not explicitly engage diffusion theory or network concepts and methods, this has changed. As one set of prominent social movement scholars declared, “Diffusion requires that movements across these multiple sites be linked together through activist networks, or at least informed and inspired by media-transmitted images or shared cultural understandings of popular struggles in other settings” (Givan et al. Reference Givan, Roberts and Soule2010: 6). Tarrow (Reference Tarrow, Givan, Roberts and Soule2010) argues that diffusion in movements is frequently complex, occurs through multiple network processes, develops in interaction with institutions, and causes shifts in the scale of collective action (local → regional → national → transnational).

Mesolevel Networks and the Diffusion of Social Movements

Some of the most influential papers on social movement diffusion have come from Peter Hedström and his colleagues, who have tackled the rise of the Swedish labor movement. Sweden was very conservative and industrialized slowly by Western European standards. Nevertheless, within a few decades, it had one of the best-organized and most successful labor movements in the world and became a standard-bearer for social democracy.

Hedström’s (Reference Hedström1994) first paper applied a spatial diffusion model to explain the spread of the trade union movement. He argued that social and geographical ecologies influence the formation of social networks in a population and, in turn, the resulting network structure influences social movements because mobilization can be contagious across places through networks. His analysis finds that in 1890 nearly all unions were located in cities. However, by 1905, unions existed in about half the districts, and most locals were in rural areas. In 1940, unions had spread to all but a few districts. Drawing on administrative and organizational data, including the founding date of the first trade union in hundreds of Swedish districts, Hedström used a hazard model to predict the first union in a district. His results suggest that spatial diffusion played an important part because, net of controls for total union density, the size of the industrial labor force, district size, and the presence of other organizations, prior union formation in proximate districts was associated strongly with adoption.

In a subsequent paper, Hedström and his colleagues reconstructed the role that social influence played in the socialist movement (Hedström et al. Reference Hedström, Sandell and Stern2000). Although the Swedish Social Democrats first appeared in 1889, it was the country’s leading electoral party with chapters in most parts of the country by the time of World War I. In the context of high uncertainty about the benefits of adoption and conservative resistance to socialism, Hedström and his colleagues proposed that multiple processes and multiplex networks explain its diffusion. The first is learning through labor organizing. As union members learned about socialism adopted elsewhere, they became more likely to found a party chapter. The second is the persuasiveness of peripatetic socialist agitators whose travels unintentionally created a “mesolevel” network that linked workers across the length and breadth of the country.

Hedström believed that these agitators were persuasive to the extent that they provided novel information in the context of latent demand for change. They further argued that the “mesolevel” network that resulted from the travels of party agitators linked districts differently than did interpersonal, microlevel networks. Overall, mesolevel networks have a low density with ties bridging long geographical and sociometric distances. The visits of socialist agitators created ties between districts that reduced the distances between them and between the neighbors of those districts. In creating these ties, the agitators thus unintentionally influenced the path of diffusion across Sweden. A computer simulation supported the proposition that diffusion would have occurred much less swiftly absent a mesolevel network of this kind.

To test the theory, they employed logit models to estimate the founding of a Social Democratic party organization in 4,566 administrative districts between 1894 and 1911. Their models predict party founding and include controls for union density, as well as the density of social and religious organizations. The results lend support to the theory, with both local and mesolevel networks influencing adoption. Counterpressures were also influential; conservative religious groups apparently hampered socialism’s adoption. Ecological factors clearly mattered; party organizations were more likely to form in cities, industrialized areas, and areas of working-class concentration. Perhaps the most interesting finding is that visits by agitators increased the odds of a party chapter in districts with few workers and low union density, suggesting two routes to Social Democratic Party adoption. One ran through local union organizing using the learning mechanism, the other through agitation using the mechanism of persuasion (or influence). Although we might expect that labor agitators were prone to visit towns where class conflict was intense, the regression models and historical evidence suggests otherwise. Agitators focused their efforts on unorganized workers and farm laborers (Hedström et al. Reference Hedström, Sandell and Stern2000: 148). Whereas this finding undercuts the notion that diffusion is more likely in the presence of latent demand, casting doubt on the primacy of learning, it boosts the causal interpretation of the relationship between visits and adoption through influence.

Communications Media and the Diffusion of Protest

In the spring of 1960, a new protest tactic swept the American South. Beginning in the city of Greensboro, North Carolina, African American protesters staged sit-ins at segregated lunch counters. Within two months, protesters had staged sit-ins in every Southern state except Mississippi. Kenneth Andrews and Michael Biggs (2006) rejected previous explanations for this tactic’s swift diffusion, which had focused on spontaneous adoption and preexisting activist communities (Morris Reference Morris1986). Instead, they proposed that movement organizations, social networks linking historically black colleges, and information about protests elsewhere fostered diffusion. Using event-history modeling to predict the first date of a sit-in in 334 Southern cities, they find little evidence that organizational networks or local movement organization explained adoption. However, they find that the hazard of sit-in adoption in a given city increased when local newspapers covered sit-ins in another city. Time and space constrained the relationship, though, with the relationship much greater when newspaper coverage of protests in a first city was covered in a second city within three days.

Andrews and Biggs argued that, although local social networks were probably important in organizing sit-ins in a given city, they do not explain why the tactic spread. Black college students adopted sit-in tactics because of news reports about protests elsewhere. They measure exposure by whether a given newspaper reporting on an event had at least 5 percent circulation in a city (p. 763), which, as a measure of penetration, tells us little about the exposure of local activists to the news. We might expect that radio or television news coverage would have been far more influential than newspapers with very modest regional circulation. Moreover, we have to be cautious about rejecting the social network diffusion hypothesis in this study because the network measure was far from robust: namely, a dummy variable for interorganizational ties between college campuses through the black Central Intercollegiate Athletic Association (p. 762). Although this captures one kind of linkage between college campuses, there were probably other, possibly more influential, ties between activists. Multiple processes and multiplex networks probably linked activists across cities and organizations, which propelled diffusion alongside newspaper coverage.

Whereas it is intuitively appealing that communication technologies spread the reach of social movements in democracies (Givan et al. Reference Givan, Roberts and Soule2010; Meyers Reference Meyers2000; Roscigno and Danaher Reference Roscigno and Danaher2001), what about in authoritarian regimes? In recent years, the role of diffusion through mass media has become an important line of comparative research. The velvet revolutions against communism in 1989, the “color revolutions” in post-Soviet states, and the Arab Spring brought attention to how foreign news broadcasts, the internet, and social media transmitted information that putatively triggered popular rebellions against authoritarian regimes (Beissinger Reference Beissinger2007; Hale Reference Hale2013; Howard Reference Howard2010; Hussain and Howard Reference Hussain and Howard2013; Weidmann Reference Weidmann2015; Weyland Reference Weyland2012). The prevailing notion is that better information fosters rebellion by providing models, injustice frames, and repertoires that aggrieved, but poorly organized citizens, can adopt. Perhaps more importantly, uncensored news can provide insight into aggregate levels of discontent in the populace that instills confidence in dissidents. Nevertheless, social influence models tend to cast doubt on the sufficiency of information. Collective actors generally require social reinforcement and multiple channels of influence before taking up something like risky protests.

A series of recent papers on the former German Democratic Republic (i.e., East Germany)—arguably a “most likely” case for foreign media’s impact in authoritarian polities—further call into question strong claims about the sufficiency of mass media to explain protest diffusion. East Germany was a rigidly controlled, authoritarian, Marxist–Leninist regime. Despite erecting a daunting surveillance and control system, East Germany was unusual in the Soviet bloc because West German television was widely available. Conventional wisdom maintains that this was the Achilles’s heel of East Germany: nearly every household had a TV. Once news reports about the Soviet bloc’s erosion and scattered protests in Leipzig and other cities flooded Eastern living rooms, the false sense of mass support for the regime evaporated, protests multiplied, and the system collapsed (Kuran Reference Kuran1991; Lohmann Reference Lohmann1994).

A paper by Holger Kern (Reference Kern2011) refutes the central tenant of this argument. Kern noted that Western television was not universally available because of topographical features and distances from broadcasting towers. This allowed him to exploit a “natural experiment” to test whether receiving West German television explains protest in East German counties. He created two groups of counties that differed as much as possible in terms of their access to West German television but were otherwise similar, dropping counties adjacent to access to limit the risk of spatial diffusion of television’s influence. His dependent variables measured protest events and participation from police reports. He used one-to-one nearest-neighbor genetic matching techniques to find good comparison units for 22 counties that lacked access to Western television. Comparing these two sets of counties from September 1989 through March 1990, Kern shows that those counties with Western television access adopted protest somewhat earlier, but they did not substantially differ from those without TV. This was true whether measured in terms of the rate of protest diffusion or its depth (the extent of protest activities measured by the number of events and the total number of participants). In a counterfactual world in which those 22 counties received Western broadcasts, there would have been no difference in the rate or depth of protest diffusion.

In a follow-up paper, Charles Crabtree, David Darmofal, and Kern (2015) take this analysis a step further by estimating the probability of protest events in the East German revolution with better measures of mass media penetration. Specifically, they use an electromagnetic signal propagation model precisely to estimate which counties fell below the threshold of receiving Western TV broadcasts. The comparison of counties above and below that threshold reveals substantial differences, including that those below the threshold experienced about a fifth fewer protest events on average than those above. Does the presence of Western TV explain the difference? To find out, they estimate Cox hazard models predicting protest events that include a host of county-level sociodemographic and economic characteristics while including spatial dependence, event dependence, and heterogeneity in a repeated events framework. Again, their findings reject the hypothesis that Western TV accounted for protest diffusion in East Germany in 1989–90.

Is the same true for other episodes of protest? In a subsequent paper, Crabtree, Kern, and Pfaff (Reference Crabtree, Kern and Pfaff2018) analyze an earlier uprising. In June 1953, East Germany experienced the Soviet bloc’s first mass uprising against Communist rule. From its inception in East Berlin, a raucous and seemingly spontaneous protest movement rapidly spread across the country. Within days, it brought the regime to its knees, requiring Red Army intervention to save it. The consensus shared by contemporary observers and historians is that Western radio broadcasts suffice to explain why popular protest spread so widely in such a short time frame. What makes this especially persuasive is that radio ownership was ubiquitous, and the United States operated a radio station as an arm of anti-Communist propaganda. Did the “Radio in the American Sector” (RIAS) and other Western broadcasters spread rebellion in the provinces by covering labor unrest in the capital? Using electromagnetic signal propagation models, Crabtree et al. estimated radio signal strength in 1 km × 1 km cells for all of East Germany by terrain characteristics, the location of transmitters, and the technical characteristics of broadcasters. Because radio reception was exogenous to other characteristics of places, it is plausible to interpret the relationship between broadcast strength and protest adoption as causal. Nevertheless, estimating probit models for protest occurrence in more than five thousand municipalities, they find no association between measures of signal strength and the probability of protest events.

They do find evidence for a rival interpretation based on spatial diffusion through social networks. Probit models strongly indicate that the greater the distance a municipality was from East Berlin, the lower its odds of experiencing protest. They account for this with historical evidence from security reports and other sources indicating that protests spread principally through interpersonal ties. In particular, train connections facilitated social diffusion as people commuting from the capital seeded local clusters of rebellion. To test this claim, they show that effective travel distance from East Berlin strongly predicts the probability of protest, with the estimated probability diminishing with increasing distance by train. Their findings suggest that the rail network’s characteristics, rather than radio broadcasts, better explains where protest diffused in June 1953.

Other case studies not only offer methodological innovations introducing better measures of mass media penetration but also theoretical modifications to network diffusion models. A good example is a study on the Arab Spring in which Navid Hassanpour (Reference Hassanpour2017) challenges a long-held assumption that successful social movements mobilize (diffuse) from the center. Using data from the Egyptian Revolution in Cairo, the Syrian Civil War in Damascus, and social network experiments, he demonstrates that mobilization is more likely to occur from the periphery than from the center under certain circumstances. In particular, when potential movement leaders are embedded within small-world networks and traditional communication channels are abruptly disrupted, mobilization is likely to shift to the social margins where individuals are generally less risk-averse, more likely to be early adopters, and less likely to have countervailing ties. In such situations, minimal cores, which Hassanpour defines as the smallest set of risk-takers who will continue to act among a majority opposed to its actions (Hassanpour Reference Hassanpour2017: 85), are more important than a critical mass. Cut off from risk-averse individuals who could dampen their enthusiasm, minimal cores located in clusters of resistance lying on the margins are more likely to continue to advocate for change. His data show that in Cairo and Damascus when internet and cell phone communications were completely and abruptly shut down, not only did protests increase but also they became more widely dispersed and locally clustered as contention shifted from the moderate center to the radical periphery. Rather than suppressing tentative coordination by people fearful of repression, the security forces confronted spontaneous protests by radicals on the margins of urban society who were far harder to intimidate.

Hassanpour’s book makes an important contribution by showing that it is not only network structures that matter but also the nature of social relations. As the Arab Spring case suggests, sometimes more communication (i.e., more ties) can work against mobilization because it links a radical minority to a risk-averse majority that drowns out “initial sparks of risk-taking” (ibid.: 72; see also Siegel Reference Siegel2009). His paper contributes to the growing awareness that social ties need not facilitate mobilization and that repressive regimes may exploit network structures and manipulate digital media to hinder protest diffusion (King et al. Reference King, Pan and Roberts2013; Kitts Reference Kitts2000; Siegel Reference Siegel2011).

Leadership and the Diffusion of Political Islam

Political Islam as a modern mass movement was born in Egypt. In a paper on the rise of Egypt’s Muslim Brotherhood, Steven Brooke and Neil Ketchley (2018) explain its rapid spread from 1928 through 1940. During that period, the Brotherhood expanded from a few provincial offices to more than two hundred chapters and spread to all but a handful of the country’s governorates (379–80; 388). To account for such rapid spatial diffusion, Brooke and Ketchley conduct an ecological analysis of the founding of Brotherhood chapters culled from movement publications. Combining year of founding with administrative data on more than four thousand districts, they estimate a multilevel logistic regression predicting a branch in 1937 and 1940. They find that, contrary to much of the literature identifying local reactive mobilization against foreigners and economic modernization as driving forces, the Brotherhood was more likely to be adopted in subdistricts with higher than average literacy rates and direct connections to the national railway network.

The analysis suggests two pathways to adoption. One is the diffusion of the movement through printed information, the other through social ties between places and the Brotherhood organization channeled through railway links. To support their proposed mechanisms, Brooke and Ketchely turn to process tracing of historical source materials to understand the movement’s spread. They describe a movement that published widely popular magazines and newsletters targeting the newly educated in provincial towns. Movement leaders intentionally exploited the railways. A crucial moment in the movement’s expansion occurred when it moved its headquarters to Cairo, the hub of the national railroad network. This allowed leading agitators to fan out across the country more efficiently (pp. 388–89). There are clear parallels between Brooke and Ketchely’s (2018: 390–91) argument and Hedström et al.’s (Reference Hedström, Sandell and Stern2000) theory of mesolevel networks, although Brooke and Ketchely’s study includes neither network data nor explicit social network analysis.

Gang Violence

Criminologists are embracing network analysis to explore various features of crime (Carrington Reference Carrington, Scott and Carrington2011). These include the association between personal networks on crime and delinquency (Haynie Reference Haynie2001; Massey and Krohn Reference Massey and Krohn1986); the relationship between network fragmentation and neighborhood crime rates (Matsueda Reference Matsueda2006; Sampson and Groves Reference Sampson and Groves1989); the social organization of crime (Baker and Faulkner Reference Baker and Faulkner1993; Smith and Papachristos Reference Smith and Papachristos2016); the trade-off between efficiency and security (Crossley et al. Reference Crossley, Edwards, Harries and Stevenson2012; Morselli et al. Reference Morselli, Giguère and Petit2007); and the crafting of intervention strategies (Cavallaro et al. Reference Cavallaro, Ficara, De Meo, Fiumara, Catanese, Bagdasar, Song and Liotta2020; Klerks Reference Klerks2001). Network data is even used to enhance prosecution (Krebs Reference Krebs2002; Sparrow Reference Sparrow1991). Of particular note is the work of Andrew Papachristos and his colleagues, who have examined numerous aspects of criminal behavior, including the diffusion of violence through gang networks. Although prior studies focused on the effect of individual (e.g., age, gender, race), situational (e.g., the presence of weapons, drugs, alcohol) and community (e.g., mobility, cohesion, inequality) factors (Papachristos et al. Reference Papachristos, Braga and Hureau2012), Papachristos was among the first to bring social network data to bear on the study of gang violence.

In an early paper, Papachristos (Reference Papachristos2009) analyzed the patterns of homicides among Chicago gangs from 1994 to 2002. In it, he builds upon Gould’s (2003) dominance theory of violence, arguing that gang violence spreads like social contagion as status disputes arise and then resolved through violence. “What begins as a single murder soon generates a dozen more as it diffuses through these murder networks” (Papachristos Reference Papachristos2009: 76). To test this, Papachristos gathered data on all Chicago homicides from 1994–2002 and selected cases in which the victim or offender was a gang member. He then aggregated these to the gang level to construct networks of gang-on-gang homicides. He also used geospatial data to map each gang’s turf because they are “typically the setting of a group’s collective memories, a meaningful geographic space for young men as they transition from childhood to adulthood” (Papachristos et al. Reference Papachristos, Hureau and Braga2013: 42—see also Whyte Reference Whyte1943). Using quadratic assignment procedure (QAP), network autocorrelation, and logistic regression, he finds that both dominance competition (measured by the degree to which two gangs’ turf overlaps) and prior exposure to violence through gang-on-gang homicide networks increase the likelihood of violence.

In a follow-up study, Papachristos, David Hureau, and Anthony Braga (2013) compared violence patterns among Chicago and Boston gangs in 2008 and 2009. As before, they aggregate their data to construct gang-on-gang violence network data. For this analysis, though, they draw on exponential random graph models (ERGMs) (Robins Reference Robins, Scott and Carrington2011; Robins et al. Reference Robins, Pattison, Kalish and Lusher2007) to disentangle dominance competition from turf disputes. Here, they distinguish dominance competition from turf in terms of actual patterns of violence. In particular, they test for the nonrandom presence of transitive triads (see figure 2), which they argue captures dominance hierarchies’ dynamics. Separately, they measure turf competition by whether gangs share turf boundaries. Interestingly, and contrary to their expectations, they find no evidence that gang violence contributes to establishing dominance hierarchies. However, they do uncover evidence that turf competition facilitates the spread of violence. Consistent with Papachristos’s earlier study, they also find that exposure to prior violence drives the spread of violence, even when gangs do not share turf boundaries.

Figure 2.

Transitive triad.

Papachristos and his colleagues have also explored the diffusion of gun violence. In one study (Papachristos et al. Reference Papachristos, Braga and Hureau2012), they examined fatal and nonfatal gunshot injuries in Boston’s Cape Verdean community from 2008 to 2009. Using FIOs (Field Intelligence Observation cards), which record noncriminal encounters between two or more individuals, they mapped interactions between the known gang members, their associates, and other individuals. They found that the greater the proportion of ties that individuals have to others who have had a gunshot injury, the more likely they will suffer the same fate. However, the farther they are from a gunshot injury (in terms of path distance), the less prone they are to being be shot. A subsequent study (Green et al. Reference Green, Horel and Papachristos2017) examined the spread of violence among individuals living in Chicago from 2006 to 2014. Beginning with 138,163 arrested individuals who were victims of gun violence, the authors constructed a “co-offending network” where individuals arrested for the same offense share a tie with one another. They found that 63.1 percent of the gunshot violence resulted from social contagion. “Subjects of gun violence were shot on average 125 days after their infector (the person most responsible for exposing the subject to gunshot violence), with a median time difference of 83 days” (ibid.: 329). Their analysis also uncovered evidence that social distance plays a role. In fact, consistent with the Christakis and Fowler studies, it found that gun violence, at least in this network, spread to three degrees of separation.

Violent Extremism

Since the 9/11 terrorist attacks, analysts have increasingly drawn on network analysis to examine “dark networks,” that is, covert, illegal, and/or clandestine networks (Asal and Rethmeyer 2008; Everton Reference Everton2012; Krebs Reference Krebs2002; Pedahzur and Perliger Reference Pedahzur and Perliger2006; Raab and Milward Reference Raab and Milward2003; van der Hulst Reference van der Hulst, Scott and Carrington2011). Many have focused on using network measures for devising intervention strategies (Carley et al. Reference Carley, Lee and Krackhardt2002; Everton Reference Everton2012; Jordan et al. Reference Jordan, Mañas and Horsburgh2008; Sageman Reference Sageman2004), but analysts have cautioned against using them blindly (Carley et al. Reference Carley, Lee and Krackhardt2002; Krebs Reference Krebs2002; Moody Reference Moody2005; Roberts and Everton Reference Roberts and Everton2011, Reference Roberts, Everton and Dawoody2016). Analysts have also considered the role that social ties play in dark network recruitment (della Porta Reference della Porta2013; Sageman Reference Sageman2004), variation in the structure of dark networks (Oliver Reference Oliver2014; Xu and Chen Reference Xu and Chen2008), and the effect of network topography on efficiency, security, and resilience (Arquilla and Ronfeldt Reference Arquilla, Ronfeldt, Arquilla and Ronfeldt2001; Bakker et al. Reference Bakker, Raab and Milward2011; Everton and Cunningham Reference Everton and Cunningham2015).

Although most of these have looked at contemporary dark networks, some have turned their lens toward the past. For example, research on the so-called radical wing of the Reformation has considered how violence diffused among predominantly nonviolent Anabaptists (forerunners of the Amish and Mennonites). Anabaptists trace their beginnings to 1524 and a small group in Zurich, later known as the Swiss Brethren (Williams Reference Williams1975). They originally followed Ulrich Zwingli’s teachings, but they eventually embraced adult baptism, which led them to be targets of violent repression (McDaniel Reference McDaniel and Wellman2007). Although they leaned toward nonviolence, in 1534, one group briefly established a violent theocracy in Münster, Westphalia, where torture and public executions became commonplace (Stayer Reference Stayer1979). In June 1535, a handful of defectors helped the local Prince-Bishop regain control of the city, after which the rebellion’s leaders were tortured and executed (McDaniel Reference McDaniel and Wellman2007).

Luke Matthews and several others (Matthews et al. Reference Matthews, Edmonds, Wildman and Nunn2013) were curious whether the violence found among Anabaptists was “inherited” or “spread.” To test for the former, they constructed a “phylogenetic” tree tracing the history of schisms among Anabaptists beginning with one denomination in 1520 and ending with thirteen in 1535, from which they calculated a “distance” between denominations that represented the total amount of time (as measured by schisms) separating them. To test the latter, they mapped the ties between the same 13 denominations, linking two if one or more of their leaders knew one another. Their analysis shows that while most theological beliefs spread across the leadership network, violence may have been inherited, leading them to suggest “a good working hypothesis is that religious violence does not arise from a group’s characteristic theological beliefs and practices. Rather, violence may be a learned trait … [or] the outcome of other factors … inherited along congregational lines” (ibid.: 13).

In a related study, Cunningham, Everton, and Murphy (Reference Cunningham, Everton and Murphy2016) use an expanded Anabaptist dataset (McLaughlin Reference McLaughlin2015) to show that the leadership network associated with the rebellion grew increasingly insular and was more likely to hold apocalyptic beliefs. Their analysis builds on an earlier study that examined the evolution of the 9/11 Hamburg cell (Everton Reference Everton2016). Both draw on Cass Sunstein’s (2002) “law of group polarization” to argue that internally dense religious groups that maintain few external ties are more likely to radicalize. And when combined with apocalyptic beliefs, such groups can turn violent—other groups exhibiting similar dynamics include the Peoples Temple, the Branch Davidians, and the Armed Islamic Group of Algeria (GIA) (Everton Reference Everton2018).

Michael Kenney’s (2018) book on the contemporary Islamist movement in Great Britain deftly employs a mixture of qualitative evidence and network analysis to identify the dynamics that lead people to adopt an extremist identity. Focusing on a Salafi-jihadist group (al Muhajiroun) active since the 1990s, Kenney used extensive fieldwork, interviews with activists, and analysis of news reports and publications to reveal “a network of deeply-committed members who sought to replace Great Britain’s secular democracy with a religious theocracy based on their interpretation of Salafism and Islamism” (ibid.: 3). Although never larger than 200 members, the group was a prominent voice in Islamic radicalism in Britain. Kenney shows how people adopted an extremist identity through a process that involved both strong and weak ties. The group established weak ties to potential recruits by staging protest events and public outreach, targeting those with a strong sense of Muslim collective identity. Once it linked them to the movement, it fostered their radicalization through gradual acculturation and nurturing strong emotional attachments.

In particular, group solidarity relied on ties to its charismatic founder, an imam noted for his extremist positions and fiery sermons. However, after this “almost cultish” leader fled Britain, the group evolved from a centralized structure toward a cell-like, small-world structure with “high local clustering and short path lengths.” Kenney demonstrates these changes by contrasting the group’s network characteristics over three periods (1996–2005, 2005–9, and 2009–12), revealing clear evidence of decentralization (degree centralization fell from .840 to .599, and betweenness centralization fell from .747 to .357). Although it proved resilient in the wake of its leader’s departure and persuaded some followers to take up arms at home and abroad, the group ultimately dwindled. Its inflexible dogmatism limited its appeal, and recruiting new members became harder in the context of surveillance.

Using a similar approach, Johannes Saal (Reference Saal2019) draws on rational choice, social capital, and network theories to explore the spread of jihadi groups in Germany, Austria, and Switzerland. His analysis reveals that all three networks grew in waves. Strong ties were more important earlier in their development than later, suggesting that larger networks may be more vulnerable to infiltration than smaller ones. Why? Because, else being equal, network density is inversely associated with network size as the number of potential ties grows exponentially with each additional node (de Nooy et al. Reference de Nooy, Mrvar and Batagelj2018). As such, larger networks tend to be sparser than small ones, and we have learned that individuals are more likely to violate group norms in sparse networks than in dense ones (Festinger et al. Reference Festinger, Schachter and Back1950; Finke and Stark Reference Finke and Stark2005; Granovetter Reference Granovetter2005). Saal also highlights the key role that Salafist preachers play in the development and spread of Jihadism. He notes that, on average, preachers score higher in terms of most centrality measures, in particular betweenness. Thus, they are more likely to be located in brokerage positions, which allows them to play crucial roles in disseminating funds, teachings, and violence (Saal Reference Saal2019: 46). His analysis of travel networks that help individuals join ISIS or other jihadi groups found that poorly constructed ones often led to failure, while well-constructed ones were more likely to lead to success. The difference, according to Saal, depends largely on whether facilitators have access to bridging social capital. That is, did they possess the ties and trust needed to connect across to numerous groups and individuals who could help foreign fighters successfully reach the conflict zone of their choice?

Conflict, Peace, and the Networks of Nations

International relations scholars have long recognized that connections between nations facilitate the diffusion of various phenomena (Maoz Reference Maoz2012), such as conflict, peace, and human rights. However, it is only in recent years that they have turned to network methods to do so (Hafner-Burton et al. Reference Hafner-Burton, Kahler and Montgomery2009; Maoz Reference Maoz2012).Footnote ⁴ Emilie Hafner-Burton and Alexander Montgomery’s (2012) paper, which explores the effect of trade agreements on international conflict, is reflective of this approach. They use longitudinal network data to explore the effects of ties on the diffusion of conflict. Here, a tie between two states indicates the number of comemberships they share in one or more preferential trade agreements (PTAs). They find that while the presence of trade agreements between two states can dampen the spread of conflict, power disparities can increase it. Their analysis models two types of power disparities: dependence and access. They measure the first in terms of the total number of trade institutions two nations belong to together and separately. Given two states, A and B, “A’s dependence on B increases if A and B join additional trade institutions together, but A’s dependence on B decreases if A joins additional trade institutions without B” (ibid.: 262–63). To capture access, they use eigenvector centrality, which measures the degree to which actors are connected to well-connected actors. Power disparities, then, are the differences between the respective dependence and access scores of two nations.

Zeev Maoz, along with his many collaborators, deserves the most credit for pushing this line of research, collecting and analyzing various types of ties between nations (e.g., alliance, conflict, trade) to explore the causes of international conflict. For example, he, along with Ranan Kuperman, Leslie Terris, and Ilan Talmud (Reference Maoz, Kuperman, Terris and Talmud2006), explored structural equivalence’s effect on conflict. Recall that structurally equivalent actors hold similar network positions and tend to behave similarly. They are identified not by direct ties to one another but by the similarity of their ties to others. Using network data from 1816 to 2001, Maoz et al. (Reference Maoz, Terris, Kuperman and Talmud2007) identified structurally equivalent actors in terms of three types of ties: alliances, trade, and shared membership in one or more international government organizations (IGOs). They found that “strategic” and “trade-based” affinity, that is, structurally equivalent states based on patterns of alliance and trade-based ties, reduces conflict, but structural affinity in terms of shared IGO membership increases it. The latter result is surprising since many scholars believe that common IGO membership reflects a shared commitment to the management of international politics and, as such, should reduce conflict. However, when Maoz et al. (Reference Maoz, Kuperman, Terris and Talmud2006) only looked at ties among politically relevant states, they found that while the results for strategic and trade-based affinity essentially remained unchanged, IGO membership structural affinity did reduce conflict after the end of World War II. Finally, in both sets of analyses, they show that integrated structural affinity (i.e., one accounting for all three types of ties) reduces conflict.

In a companion article (Maoz et al. Reference Maoz, Terris, Kuperman and Talmud2007), the same authors drew on balance theory to explore the effect of balanced and imbalanced triads of nations on the diffusion of conflict. In the international arena, balance occurs when “an ally of an ally is also an ally” or “an enemy of an enemy is an ally,” and imbalance is where “an ally of an ally is an enemy” or “an enemy of an enemy is also an enemy.” Although networks gravitate toward balance (Cartwright and Harary. Reference Cartwright and Harary1956; Davis Reference Davis1967; Heider Reference Heider1946) imbalances can and do occur. Their analysis identifies numerous causes of imbalance (e.g., strategic rivalry, opportunism, contiguity) and balance (e.g., economic interdependence, shared IGO memberships, joint democracy). More importantly, at least for our purposes here, it finds that international relational imbalances reduce alliance formation and increase the spread of conflict.

Maoz (Reference Maoz2011) also draws on network analysis to examine the tendency among democracies to avoid conflict with one another. Known as the “democratic peace” (Russett and Oneal Reference Russett and Oneal2001), it is probably the closest thing “to an empirical law in international relations” (Levy Reference Levy1988: 662). However, Maoz notes that while this is true, democracies are just as conflict-prone as nondemocracies, and the greater the proportion of democracies in the international system does not lower the overall level of conflict (Maoz Reference Maoz2011: 251). To resolve this paradox, he analyzes the international system at several levels. Beginning with what he calls strategic reference networks (SRNs), which are ties among states that are of strategic relevance to one another, he derives two types of subnetworks: strategic reference groups (SRGs) and cliques (SRCs). A nation’s SRG is its ego-network, that is, its direct ties to other nations within its SRN and the ties between them. A nation’s SRCs are the various cliques to which it belongs within its SRN.Footnote ⁵ Maoz finds that SRG size is positively associated with conflict, while the proportion of allies within an SRG has the opposite effect. He also shows that the average level of democracy in the SRGs of democratic states lowers the spread of conflict, but the outcome is mixed in SRGs of primarily of nondemocratic states. Finally, he finds that democracies belonging to numerous SRCs (essentially those that are central within the international network) have a larger impact on democratization’s spread than those belonging to fewer (ibid.: 270).

A difficulty analysts face when exploring the relationship between democratization and peace is that it is unclear whether democratization results from conflicts resolved through treaties (social influence) or if democracies are more likely to form alliances with other democracies (social selection). Existing research offers evidence for both. To disentangle these influence and selection effects, Camber Warren (Reference Warren2016) has drawn on coevolution SAOMs (Steglich et al. Reference Steglich, Snijders and Pearson2010) to examine the interdependent relationship between military alliances, international conflict, and democratization from 1920 to 2000. His models find evidence for both selection and influence. States with similar regime types are more prone to form alliances with one another.Footnote ⁶ Democratic states are also less likely to engage in military disputes, and nondemocratic states that ally with democratic regimes are more likely to democratize. However, “military conflict between states tends to inhibit the development of democratic regimes” (Warren Reference Warren2016: 435), thus challenging the results of some earlier studies. In short, evidence for the democratic peace exists, but network interdependencies make the relationship between conflict, alliances, and democratization complex.