![]() įor studying the robustness of clustered networks a percolation approach is developed. ![]() For networks with high clustering, strong clustering could induce the core–periphery structure, in which the core and periphery might percolate at different critical points, and the above approximate treatment is not applicable. This indicates that for a given degree distribution, the clustering leads to a larger percolation threshold, mainly because for a fixed number of links, the clustering structure reinforces the core of the network with the price of diluting the global connections. Watts and Steven Strogatz introduced the measure in 1998 to determine whether a graph is a small-world network.Ī graph G = ( V, E ) ![]() The local clustering coefficient of a vertex (node) in a graph quantifies how close its neighbours are to being a clique (complete graph). In a valued graph, values are added to the ties to indicate, for example, the importance of a tie. This impliesthat the matrix A is not necessarily symmetric. In a directed graph, the ties are directed from one node to another. In a discrete graph, the matrix A indicates only whether certain ties exist, i.e., the elements of A are 0 or 1. Finally, none of the possible connections among the neighbours of the blue node are realised, producing a local clustering coefficient value of 0. Social Network Analysis and Game Theory 33 A. In the middle part of the figure only one connection is realised (thick black line) and 2 connections are missing (dotted red lines), giving a local cluster coefficient of 1/3. In the top part of the figure all three possible connections are realised (thick black segments), giving a local clustering coefficient of 1. In the figure, the blue node has three neighbours, which can have a maximum of 3 connections among them. ![]() The local clustering coefficient of the blue node is computed as the proportion of connections among its neighbours which are actually realised compared with the number of all possible connections. Example local clustering coefficient on an undirected graph. In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. ![]()
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