Well, if I remember my graph theory well enough, if A is the adjacency matrix of the graph, each entry of A^n is the number of ways to get between the corresponding nodes in n steps or less. So ...

This is a survey paper on the second largest eigenvalue λ₂ of the adjacency matrix of a graph. Among the topics presented are the graphs with small λ₂, bounds for λ₂, algebraic connectivity, graphs ...

We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G n ) n≥0 converging locally to a Galton—Watson tree T (GWT), we provide an explicit formula ...