On the Limiting Behavior of Parameter-Dependent Network Centrality Measures

We consider a broad class of walk-based, parameterized node centrality measures based on functions of the adjacency matrix. These measures generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be “tuned” to interpolate between degree and eigenvector centrality, which appear as limiting cases. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones.