Analyzing the Similarity-Based Clusterability of the Vertices in a Complex Network

We propose an approach to quantify the extent to which vertices in a complex network are clusterable on the basis of the similarity of the values with respect to two or more node-level metrics. We use the Hopkins Statistic to assess the clusterability and consider the centrality metrics as the node-level metrics. Our approach is to construct a logical topology of the vertices in the complex network using the normalized values of the centrality metrics as coordinates and determine the Hopkins Statistic for such a logical topology of the vertices. Our hypothesis is that if two or more vertices in a complex network have similar values for the centrality metrics, then the vertices should be clusterable to one or more clusters due to their proximity to each other in the normalized centrality-based coordinate system. The value for the Hopkins Statistic measure (ranges from 0 to 1) for such a logical topology of the vertices should be high, and vice-versa. We evaluate the Hopkins Statistic for 47 real-world complex networks (of diverse degree distributions) with respect to the neighborhood-based and shortest path-based centrality metrics. We observe the neighborhood centrality-based logical topologies of the vertices to incur relatively larger Hopkins Statistic values (i.e., exhibit higher similarity-based clusterability) for a majority of the networks.