Ranking nodes in graphs is of much recent interest. Edges, via the graph Laplacian, are used to encourage local smoothness of node scores in SVM-like formulations with generalizat...
We will consider balanced directed graphs, i.e., graphs of binary relations, for which the number of inputs and number of outputs are the same for each vertex. The commutative diag...
We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erd¨os-R´enyi graph G(N, c/N) and r...
Let P be a family of dipaths. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minim...
We consider a random subgraph Gp of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function...