start with an initial graph. define a candidate triangle to be a triplet of nodes with exactly two edges. for each candidate triangle, add a third edge completing the triangle with probability p. adding the edge might create more candidate triangles to the list for consideration. a pair of nodes without an edge between them might be part of multiple candidate triangles, so it might have multiple chances, each with probability p, to become connected.
goal is to add clustering, a small-world network property, to a graph which might not have it. start with an Erdos-Renyi random graph, or a Barabasi-Albert or other preferential attachment random graph.
this is a dual of the Watts-Strogatz algorithm for generating small-world networks. Watts-Strongatz starts with a graph which already has clustering and then lowers its diameter, another small-world network property.
although Watts-Strogatz is typically initialized with a ring lattice graph, it can actually be initialized with any graph that has clustering, for example a chess king lattice graph. however, it retains an imprint of its initial graph, which is undesirable if you want a random or random-looking small-world graph.
No comments :
Post a Comment