On Spectral Analysis of Directed Signed Graphs

TL;DR

This paper develops a spectral analysis framework for directed signed graphs, deriving theoretical approximations and proposing a spectral clustering algorithm that effectively partitions such networks.

Contribution

It introduces the first spectral analysis of directed signed graphs, deriving approximations and a clustering algorithm validated on synthetic and real data.

Findings

Theoretical approximations accurately capture spectral properties.

Negative edges influence node spectral projections significantly.

The proposed clustering algorithm outperforms existing methods.

Abstract

It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we derive theoretical approximations of spectral projections from such directed signed networks using matrix perturbation theory. We use the derived theoretical results to study the influences of negative intra cluster and inter cluster directed edges on node spectral projections. We then develop a spectral clustering based graph partition algorithm, SC-DSG, and conduct evaluations on both synthetic and real datasets. Both theoretical analysis and empirical evaluation demonstrate the effectiveness of the proposed algorithm.