Toward an Optimal Solution to the Network Partitioning Problem

Abstract

This paper delves into the realm of community detection in network science and graph theory with the overarching objective of unraveling the underlying structures between nodes within a network. In this pursuit, we put forth a novel and comprehensive approach to ascertain the optimal solution to maximizing the renowned community quality metric known as Max-Min Modularity. Through a series of experiments encompassing diverse case studies, we substantiate the efficacy and validity of our proposed approach, further bolstering its credibility.

Gain and Pain in Graph Partitioning: Finding Accurate Communities in Complex Networks

“…The naive dependency on an oracle for determining the complementary graph, as well as the not-very-successful heuristic hierarchy algorithm used in [9] for maximizing the Max-Min Modularity measure, directed Ferdowsi et al in [15,16] to provide a more structured way to address the deficiencies. Their focus was on methodically structuring an effective complementary graph that accurately reflects the absence of connections between nodes.…”

“…In contrast, Ref. [15] theoretically developed and solved an equivalent yet sparse integer model, determining the exact solution to the problem. Consequently, whereas [16] succeeded in deriving community structure in a prompt manner due to the heuristic fashion employed, Ref.…”

“…Consequently, whereas [16] succeeded in deriving community structure in a prompt manner due to the heuristic fashion employed, Ref. [15] achieved more precise results by obtaining optimal solutions to the integer model.…”

“…Both approaches yielded promising results, particularly those presented in [15], as they optimally solve a corresponding integer model. Nevertheless, several potential downsides exist.…”

“…This involves first defining or selecting a specific metric, referred to as a quality function, to assess the excellence of communities; then, the devising of an optimization algorithm to detect communities by optimizing the chosen quality function. Global optimization procedures, such as mathematical programming approaches [15,16], provide accurate results. However, they face computational challenges when dealing with large networks [17].…”