Complex Networks

Social Networks

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Figure 11.9: A resistor network

11.4.2 Resistor Networks

Newman et al. proposed two other methods to detect community structure in net-

works [9]. In the resistor networks method, the network is considered as an electrical

circuit in which each edge is assigned a unit resistance and pair of nodes act as unit

voltage sources and voltage sinks. Given a graph G(V,E) representing the network,

we can calculate the current through an edge e

x

∈ E for a unit voltage source s ∈V

and sink t ∈ V using Kirchoff’s current and voltage laws which state that the sum

of currents entering a node should equal the sum of currents exiting th ...