Clique counts for network similarity

TL;DR

The paper addresses efficient graph similarity by leveraging clique-based features rather than costly full graphlet counts. It introduces clique profiles built from normalized $k$-clique counts, extended by the higher-order $k$-clustering coefficients, and employs the Pivoter algorithm to obtain exact clique counts up to $k=10$, optionally augmented with the global clustering coefficient. Empirically, clique profiles yield competitive classification accuracy on several ego-network datasets and approach graphlet-kernel performance in many cases, while offering lower computational overhead. The work highlights the practicality of clique-based similarity for social networks and outlines avenues for extending the approach to sparser graphs and higher-order structures.

Abstract

Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in graphlet counts as a method for graph similarity in social networks. Higher-order clustering coefficients and the Pivoter algorithm for exact clique counts are employed

Figures (1)

• Figure 1: The change of the $k$-clustering coefficients of five networks retrieved from SNAP snap, where each edge is associated with a time-stamp. We sort the edges and treat each large network as a sequence of 120 evolving networks with equal-size edge increments; every network has a fixed amount of edge growth from the previous network. We record their $k$-clustering coefficients up to $k=25$. The vertical axis indicates the $k$-clustering coefficient, the horizontal axis corresponds to the $i$-th network in the sequence, and the label indicates the size increment.