Detecting hotspots in network data based on spectral graph theory

Abstract

Detection of hotspots (also known as dense subgraphs) in network data is an important data analysis problem due to it's significance in many contemporary applications. Clique-based formulation of this problem employing maximum flow implementation turns out to be an optimization task limiting the solution to be an approximate one. On the other hand, an iterative method building the hotspots (dense sub-graphs) in an incremental manner starting from primitive graph entities looks more practical and more conducive to incorporating application specific characteristics of interest. Motivated by this idea, we propose a novel algorithm for detecting dense sub-graphs based on spectral graph theory. The underlying principle is that the largest eigenvalue of a graph is a numerical indicator of the inherent dense connectivity. Accordingly, our algorithm starts from the egonets (sub-graphs) of individual nodes and determines the dense egonets as the primitive entities based on their eigenvalues. It then discovers hotspots (dense sub-graphs) through iterative merging of the dense egonets in a controlled manner. Experimental evaluation on benchmark graph data sets demonstrates the efficacy of the proposed method.