The neighbourhood function NG(t) of a graph G gives, for each t ∈ N, the number of pairs of nodes x, y such that y is reachable from x in less that t hops. The neighbourhood fun...
We present SNAP (Small-world Network Analysis and Partitioning), an open-source graph framework for exploratory study and partitioning of large-scale networks. To illustrate the c...
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hy...
An edge-labeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label seq...
In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to cluster...