Skip to main content Accessibility help
×
Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-08T01:49:23.899Z Has data issue: false hasContentIssue false

3 - Network Summaries

from Part I - Basic Setting

Published online by Cambridge University Press:  11 June 2026

A. D. Barbour
Affiliation:
Universität Zürich
Gesine Reinert
Affiliation:
University of Oxford
Get access

Summary

The chapter introduces some of the statistics most commonly used to describe networks. These can be seen as analogues, in a network context, of quantities such as mean and standard deviation for a sample of real numbers. They can be roughly divided into two categories: topological summaries, such as the collection of degrees of the vertices of the network, that could be derived from a picture of the network, and spectral summaries, such as the eigenvector centrality, that are derived from the spectral decomposition of the adjacency matrix of the network (or of one or more related matrices). Many of them, such as clustering coefficients, can be formulated as local summaries, computed at each vertex of the network and can then be combined to yield a global value characteristic of the entire network. The results of a number of the summaries are compared with one another, using the Florentine marriage network as an example.

Information

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×