The Right Way to Search Evolving Graphs

TL;DR

This paper introduces a BFS algorithm tailored for evolving graphs, accurately counting temporal paths and avoiding miscounts caused by naive matrix unfoldings, with applications in citation network analysis.

Contribution

It presents a novel BFS algorithm for evolving graphs that correctly accounts for temporal paths, improving over naive adjacency matrix methods.

Findings

The algorithm accurately counts temporal paths in evolving graphs.

Naive adjacency matrix unfoldings miscount paths, leading to errors.

Application to citation networks demonstrates practical utility.

Abstract

Evolving graphs arise in problems where interrelations between data change over time. We present a breadth first search (BFS) algorithm for evolving graphs that computes the most direct influences between nodes at two different times. Using simple examples, we show that naive unfoldings of adjacency matrices miscount the number of temporal paths. By mapping an evolving graph to an adjacency matrix of an equivalent static graph, we prove that our generalization of the BFS algorithm correctly accounts for paths that traverse both space and time. Finally, we demonstrate how the BFS over evolving graphs can be applied to mine citation networks.