# On Spectral Analysis of Directed Signed Graphs

arXiv: https://arxiv.org/abs/1612.08102 · HTML: https://mlsanity.com/paper/1612.08102/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2016.

## Built on by (most cited first, 4 of 4)

- [SDGNN: Learning Node Representation for Signed Directed Networks](https://mlsanity.com/paper/2101.02390/) (2021)
- [Signed Bipartite Graph Neural Networks](https://mlsanity.com/paper/2108.09638/) (2021)
- [Unraveling the graph structure of tabular data through Bayesian and spectral analysis](https://mlsanity.com/paper/2110.01421/) (2021)
- [Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphs](https://mlsanity.com/paper/2406.01517/) (2024)

## Abstract (arXiv)

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.