Fig. 5

Schematic illustrating the difference between effective resistance Ω and contraction importance Ψ in a gendered bipartite authorship network. This example network has the basic structure of the bipartite authorship network we studied: a collection of publications (represented by the black nodes) connected to their authors (represented by the nodes with colors corresponding to their assigned gender labels: , and ). Both effective resistance and contraction importance quantify the importance of an edge to diffusion in the network, albeit in different ways. The effective resistance Ω takes one of two values throughout the entire example network: either 1.00 (if its removal would disconnect nodes joined by that edge) or 0.75 (if the edge participates in a K_2,2 substructure). In contrast, the contraction importance Ψ is sensitive to the edge position relative to the rest of the network; an edge whose removal splits a network into two components with \(n_{A}^{}\) and \(n_{B}^{}\) nodes has importance \(\Psi = n_{A}^{} n_{B}^{}/n_{A\cup B}^{}\). For example, an isolated edge has Ψ=0.50 and an edge that connects to the giant component via one node has Ψ→1. In addition, edges that are more integral to the horizontal diffusion are given a higher Ψ. For instance, compare the edge near the center with Ψ=1.17 and the edge to its right with Ψ=0.50; the former is clearly more important for communicating between the left and right portions of the network, despite the fact that they both have Ω=0.75