Anomaly, reciprocity, and community detection in networks

TL;DR

This paper introduces a probabilistic generative model for network anomaly detection that incorporates community structure and reciprocity, offering a detailed understanding of edge relationships and practical algorithms for sparse networks.

Contribution

It presents a novel probabilistic approach modeling edge pairs with exact joint distributions, emphasizing reciprocity's role and providing an efficient implementation for sparse networks.

Findings

Model captures exact edge relationships

Highlights importance of reciprocity in networks

Provides efficient algorithms for sparse data

Abstract

Anomaly detection algorithms are a valuable tool in network science for identifying unusual patterns in a network. These algorithms have numerous practical applications, including detecting fraud, identifying network security threats, and uncovering significant interactions within a dataset. In this project, we propose a probabilistic generative approach that incorporates community membership and reciprocity as key factors driving regular behavior in a network, which can be used to identify potential anomalies that deviate from expected patterns. We model pairs of edges in a network with exact two-edge joint distributions. As a result, our approach captures the exact relationship between pairs of edges and provides a more comprehensive view of social networks. Additionally, our study highlights the role of reciprocity in network analysis and can inform the design of future models and algorithms. We also develop an efficient algorithmic implementation that takes advantage of the sparsity of the network.