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 ...

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 ...

In this thesis, we study sampling and weighted counting of bipartite matchings and directed acyclic graphs (DAGs). The total weight of perfect matchings of a bipartite graph equals the permanent of ...