Recovery of Vertex Orderings in Dynamic Graphs: Algorithms for a General Solution

Dynamic networks model important processes in diverse applications, from spread of infectious diseases to flow of capital in economic systems. The arrival order of nodes in such networks reveals critical insights into their structural and functional organization. In typical applications, the state of a dynamic network is available as a snapshot in time, and one must infer a node arrival order from it. We formulate a more general problem that infers a partial order or clusters of node arrivals. We provide nearly-optimal and approximate solutions to the associated optimization problem that is suitable for any dynamic graph model with only node and edge additions. Finally our methods are validated for a particular graph model through experiments on both synthetic and real-world networks.