from Part I - Basic Setting
Published online by Cambridge University Press: 11 June 2026
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.
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