Figure 3

Local node entropy. A commuting network where the sub-graph at node \(v_{1}\) is highlighted with in-flows in red, and out-flows in blue.The network consists of nodes with different degree and link weight distributions to explore the different results and normalisation approaches. Diagrams for in-flows frequency distribution f(w) at every node are in red, and out-commuting f(w) are in blue. Entropy and normalised values corresponds to: (*) = \(H_{L}^{in}\), (**) = \(H_{L}^{in} /H_{\text {deg}}^{in}\) or \(H_{L}^{out} /H_{\text {deg}}^{out}\) , and (***) = \(H_{L}^{in} /H_{Mpd}\) or \(H_{L}^{out} /H_{Mpd}\) . As an example, a uniform distribution of in-flows and a \(deg_{in}\)= 2 on \(v_{1}\) results in a maximum 1 for (**) and 0.5 for (***), whereas a uniform weight distribution and a maximum possible \(deg_{in}\) = 4 of node \(v_{5}\) results in a maximum 1 for (**) and (***).