An egonet-based approach to effective weighted network comparison

2024-10-04

arXiv.org

AI Summary

Existing weighted graph similarity measures often rely on node alignment or neglect edge weights, resulting in low structural fidelity and poor generalization. This paper proposes a node-alignment-free framework for measuring weighted network dissimilarity, which constructs graph embeddings from weighted statistical features of local ego networks—such as distance-weighted degree and neighbor weight distribution—and quantifies feature distribution divergence via the Wasserstein distance. By circumventing binary conversion and explicit matching assumptions, the method enables unsupervised comparison of weighted graphs with heterogeneous sizes. Evaluated on diverse synthetic and real-world weighted network benchmarks, it achieves state-of-the-art classification accuracy. It successfully identifies financial turbulence anomalies in stock correlation time series and quantitatively assesses how filtering strategies affect local structural fidelity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary, for example, to identify networks with comparable characteristics or to spot anomalous instants in a time sequence of graphs. While a large number of metrics are available for binary networks, the set of comparison methods capable of handling weighted graphs is much smaller. Yet, the strength of connections is often a key ingredient of the model, and ignoring this information could lead to misleading results. In this paper we introduce a family of dissimilarity measures to compare undirected weighted networks. They fall into the class of alignment-free metrics: as such, they do not require the correspondence of the nodes between the two graphs and can also compare networks of different sizes. In short, they are based on the distributions, on the graph, of a few egonet features which are easily defined and computed: the distance between two graphs is then the distance between the corresponding distributions. On a properly defined testbed with a pool of weighted network models with diversified characteristics, the proposed metrics are shown to achieve state-of-the-art performance in the model classification task. The effectiveness and applicability of the proposed metrics are then demonstrated on two examples. In the first, some"filtering"schemes -- designed to eliminate non-significant links while maintaining most of the total weight -- are evaluated in their ability to produce as output a graph faithful to the original, in terms of the local structure around nodes. In the second example, analyzing a timeline of stock market correlation graphs highlights anomalies associated with periods of financial instability.

Problem

• Weighted Graph Comparison
• Edge Intensity
• Similarity Measurement

Innovation

• Dissimilarity Measure
• Weighted Graphs
• Financial Anomaly Detection