Minimum Rank, Zero Forcing Number and Network Propagation

A graph consists of vertices and edges. An edge connects a pair of vertices. The minimum rank of a graph G is the smallest rank that can be achieved by a symmetric matrix whose graph is G. The computation of the minimum rank of a graph is equivalent to that of the maximum co-rank of the graph. It is know that the zero forcing number of a graph is an upper bound on the maximum co-rank of the graph. In this presentation we introduce the zero forcing number of a graph and its relation to the minimum rank of the graph, and show how we can use the zero forcing number in the study of network propagation