You're reading from Applying Math with Python - Second Edition

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Published inDec 2022

PublisherPackt

ISBN-139781804618370

Edition2nd Edition

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Sam Morley

Quantifying clustering in a network

There are various quantities associated with networks that measure the characteristics of the network. For example, the clustering coefficient of a node measures the interconnectivity between the nodes nearby (here, nearby means connected by an edge). In effect, it measures how close the neighboring nodes are to forming a complete network or clique.

The clustering coefficient of a node measures the proportion of the adjacent nodes that are connected by an edge; that is, two adjacent nodes form a triangle with the given node. We count the number of triangles and divide this by the total number of possible triangles that could be formed, given the degree of the node. Numerically, the clustering coefficient at a node, , in a simple unweighted network is given by the following equation:

Here, is the number of triangles at and the denominator is the total possible number of triangles at . If the degree of (the number of...

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Applying Math with Python - Second Edition

Published in: Dec 2022Publisher: PacktISBN-13: 9781804618370

Author (1)

Sam Morley

Sam Morley is an experienced lecturer in mathematics and a researcher in pure mathematics. He is currently a research software engineer at the University of Oxford working on the DataSig project. He was previously a lecturer in mathematics at the University of East Anglia and Nottingham Trent University. His research interests lie in functional analysis, especially Banach algebras. Sam has a firm commitment to providing high-quality, inclusive, and enjoyable teaching, with the aim of inspiring his students and spreading his enthusiasm for mathematics.
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Quantifying clustering in a network

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