DELTACON: A Principled Massive-Graph Similarity Function

TL;DR

DeltaCon is a scalable, principled graph similarity measure that effectively detects connectivity changes in graphs, outperforming existing methods and enabling applications like brain connectivity analysis and anomaly detection.

Contribution

The paper introduces DeltaCon, a novel graph similarity function that satisfies key axioms, is scalable, and demonstrates superior performance on synthetic and real-world graphs.

Findings

DeltaCon outperforms existing similarity measures in detecting graph changes.

DeltaCon successfully classifies brain connectivity related to creativity.

DeltaCon effectively detects temporal anomalies in email communication networks.

Abstract

How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). Experiments on various synthetic and real graphs showcase the advantages of our method over existing similarity measures. Finally, we employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.