Multi-Stage Graph Peeling Algorithm for Probabilistic Core Decomposition

TL;DR

This paper introduces a multi-stage graph peeling algorithm (M-PA) that enhances probabilistic core decomposition by focusing on dense subgraphs, improving efficiency while maintaining the quality of the results.

Contribution

The paper proposes a two-stage data screening process added to existing probabilistic core decomposition to better target dense subgraphs and improve computational efficiency.

Findings

M-PA is more efficient than the previous PA.

Proper filtering thresholds yield similar dense subgraphs as the original PA.

M-PA effectively reduces graph complexity without losing key dense structures.

Abstract

Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core decomposition algorithm based on graph peeling and Central Limit Theorem (CLT) that is capable of handling very large graphs. Their proposed peeling algorithm (PA) starts from the lowest degree vertices and recursively deletes these vertices, assigning core numbers, and updating the degree of neighbour vertices until it reached the maximum core. However, in many applications, particularly in biology, more valuable information can be obtained from dense sub-communities and we are not interested in small cores where vertices do not interact much with others. To make the previous PA focus more on dense subgraphs, we propose a multi-stage graph peeling algorithm (M-PA) that has a two-stage data screening procedure added before the previous PA. After removing vertices from the graph based on the user-defined thresholds, we can reduce the graph complexity largely and without affecting the vertices in subgraphs that we are interested in. We show that M-PA is more efficient than the previous PA and with the properly set filtering threshold, can produce very similar if not identical dense subgraphs to the previous PA (in terms of graph density and clustering coefficient).