MET: A Fast Algorithm for Minimizing Propagation in Large Graphs with Small Eigen-Gaps

Given the topology of a graph G and a budget k, how can we quickly find the best k edges to delete that minimize dissemination in G? Stopping dissemination in a graph is important in a variety of fields from epidemiology to cyber security. The spread of an entity (e.g., a virus) on an arbitrary graph depends on two properties: (1) the topology of the graph and (2) the characteristics of the entity. In many settings, we cannot manipulate the latter, such as the entity’s strength. That leaves us with modifying the former (e.g., by removing nodes and/or edges from the graph in order to reduce the graph’s connectivity). In this work, we address the problem of removing edges. We know that the largest eigenvalue of the graph’s adjacency matrix is a good indicator for its connectivity (a.k.a. path capacity). Thus, algorithms that are able to quickly reduce the largest eigenvalue of a graph often minimize dissemination on that graph. However, a problem arises when the differences between the largest eigenvalues of a graph are small. This problem, known as the small eigen-gap problem, occurs often in social graphs such as Facebook postings or instant messaging (IM) networks. We introduce a scalable algorithm called MET (short for Multiple Eigenvalues Tracking), which efficiently and effectively solves the small eigen-gap problem. Our extensive experiments on different graphs from various domains show the efficacy and efficiency of our approach.