We describe an algorithm for clustering using a similarity graph. The algorithm (a) runs in O(n log3 n + m log n) time on graphs with n vertices and m edges, and (b) with high pro...
We consider the problem of finding a maximum independent set in a random graph. The random graph G, which contains n vertices, is modelled as follows. Every edge is included inde...
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relati...
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n, p) in the critical window, that is, for p = n−1 + λn−4/...
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...