Customer Analysis with Network Science

A pairwise plot of clustering coefficient, degree, eigenvector centrality and Katz centrality of each node in the review network..The plots in the diagonal are the probability density functions of the metric.It is noticeable that in most of the plots, there exists two distinct clusters separated by an area of low density..The Katz centrality vs..clustering coefficient plot is shown in Figure 3 after running through a clustering algorithm to separate the nodes into two classes: green (24,201 nodes) and blue (821 nodes).Figure 3..Two clusters identified with the DBSCAN clustering algorithm.With the nodes identified and tagged as ‘green’ or ‘blue’, the metrics are replotted against each other, as shown in Figure 4..The node classes from the Katz centrality vs clustering plot are separated into the same distinct clusters seen in the other pairwise plots..This confirms that the mechanism(s) causing the clustering phenomenon is consistent for each metric pair..That is, a node’s class membership in a cluster in one of the graphs is dependent on its membership in the others.Figure 4..Pairwise plots with cluster membership..Clockwise from top-left: Katz vs eigenvector centrality, log(degree) vs log(betweenness centrality), clustering coefficient vs degree, Katz centrality vs degree.One particularly noteworthy observation is the clustering in the Katz vs eigenvector centrality plot..Katz centrality is calculated nearly the same way as eigenvector centrality, with the distinction that nodes are initially given “free” centrality..The plot suggests that this free initial centrality boosts the blue nodes’ Katz centrality more than that of the green nodes with comparable eigenvector centrality.There are two properties of the network that can explain this.. More details

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