Changing Volumes and Shortest Paths

As the volume of hemolymph in the hemocoel rises and falls, the shortest paths between the most distant vertices, varies. Newman, Watts and Strogatz (2001) studied the minimum path length, L, averaged over all pairs of vertices in graphs to find an abrupt transition in L as the 'rewiring' probability increased. L, maximal in a regular lattice, fell steeply when they rewired just a few of the edges. Watts and Strogatz defined a clustering coefficient, C. To calculate C, list all the neighbors of a vertex, count the edges linking those neighbors, and then divide this number by the maximum number of edges that can exist among the neighboring vertices. The operation repeats for all vertices, and the average is taken. In contrast to the path length L, the clustering coefficient remains large until the rewiring probability is quite high, so that over a wide range of p values, local connections between nearby vertices dominate the graph, but a few shortcuts provide for the necessary long-range connections.

0 0

Post a comment