A company's internal email network joins two of its employees when they have…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Networks as graphs: degree, distance and clustering

Problem

A company's internal email network joins two of its N=2000N = 2000 employees when they have exchanged messages in both directions during one month. Every employee lies in one connected piece, the mean degree is ⟨k⟩=20\langle k\rangle = 20, and breadth-first search gives a mean distance ℓ=3.1\ell = 3.1. The local-average clustering coefficient is C=0.35C = 0.35. ((a)) Estimate the clustering coefficient of a randomly wired network with the same NN and ⟨k⟩\langle k\rangle, and say how many times more clustered the email network is. ((b)) Take the tree estimate ln⁡N/ln⁡⟨k⟩\ln N/\ln\langle k\rangle as the mean distance of a randomly wired network of the same NN and ⟨k⟩\langle k\rangle. Compare the measured ℓ\ell with it, and judge whether this network is both a small world and clustered, in the sense of this chapter. ((c)) Explain why the eigenvector centrality of this network can be taken with every entry strictly positive, naming the property of the network the argument needs.

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