For a weighted, undirected graph G = V;E where jVj = n and jEj = m, we examine the single most vital edge with respect to two measurements related to all-pairs shortest paths APSP....
A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
We analyze the structure of random graphs generated by the geographical threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, a...
We analyze the properties of Small-World networks, where links are much more likely to connect “neighbor nodes” than distant nodes. In particular, our analysis provides new re...
Let G be a graph embedded in the L1-plane. The stretch factor of G is the maximum over all pairs of distinct vertices p and q of G of the ratio LG 1 (p, q)/L1(p, q), where LG 1 (p...