Universal Behavior of Load Distribution in Scale-Free Networks

TLDR: It is conjecture that the load exponent is a universal quantity to characterize scale-free networks and valid for both undirected and directed cases.

Abstract: We study a problem of data packet transport in scale-free networks whose degree distribution follows a power law with the exponent $\ensuremath{\gamma}$. Load, or ``betweenness centrality,'' of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices sends and receives a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power law with the exponent $\ensuremath{\delta}\ensuremath{\approx}2.2(1)$, insensitive to different values of $\ensuremath{\gamma}$ in the range, $2l\ensuremath{\gamma}\ensuremath{\le}3$, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.