The Right Way to Search Evolving Graphs

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.