Nodal domain partition and the number of communities in networks

TL;DR

This paper introduces a novel method based on Discrete Nodal Domain Theory to accurately determine the number of communities in complex networks and partition them effectively using spectral properties.

Contribution

It proposes a new spectral clustering approach leveraging Laplacian eigenvectors and nodal domain theory for community detection in networks.

Findings

Effective in determining the number of communities.

Fast and applicable to real network datasets.

Provides a topological and geometric basis for partitioning.

Abstract

It is difficult to detect and evaluate the number of communities in complex networks, especially when the situation involves with an ambiguous boundary between the inner- and inter-community densities. In this paper, Discrete Nodal Domain Theory could be used to provide a criterion to determine how many communities a network would have and how to partition these communities by means of the topological structure and geometric characterization. By capturing the signs of certain Laplacian eigenvectors we can separate the network into several reasonable clusters. The method leads to a fast and effective algorithm with application to a variety of real networks data sets.