# A spectral method for bipartizing a network and detecting a large anti-community

## TL;DR

This paper introduces a spectral method to approximate networks by bipartite structures and detect large anti-communities, aiding in understanding complex network relationships.

## Contribution

It presents a novel spectral algorithm that efficiently finds the closest bipartite network and detects large anti-communities within a given network.

## Key findings

- Successfully approximates networks by bipartite structures
- Identifies large anti-communities in networks
- Provides an efficient optimization-based algorithm

## Abstract

Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover structural properties of a network. A network is said to be bipartite if its nodes can be subdivided into two nonempty sets such that there are no edges between nodes in the same set. It is a difficult task to determine the closest bipartite network to a given network. This paper describes how a given network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems. The algorithm also produces a node permutation which makes the possible bipartite nature of the initial adjacency matrix evident, and identifies the two sets of nodes. We finally show how the same procedure can be used to detect the presence of a large anti-community in a network and to identify it.