Robust network design

Ghayoori, A.; Leon-Garcia, Alberto

doi:10.1109/icc.2013.6654892

Cited by 5 publications

(1 citation statement)

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“…, λ n are the eigenvalues for T . We note in passing that Kemeny's constant has arisen in a variety of applied settings, including consensus algorithms [6], economics [10], vehicle traffic networks [4] and wireless network design [5].…”

Section: Introductionmentioning

confidence: 99%

Complete multipartite graphs and Braess edges

Kirkland

2019

Linear Algebra and its Applications

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Given an irreducible stochastic matrix T , Kemeny's constant κ(T ) measures the expected number of steps from any initial state to a randomly chosen final state, and is thus regarded as an indicator of the overall transit efficiency of the corresponding Markov chain. For a random walk on a connected graph with twin vertices, we present a formula for the change in Kemeny's constant after the insertion of an edge between the twins. Using that result, we investigate the circumstances under which inserting a new edge increases Kemeny's constant. In particular, we characterise the complete multipartite graphs without dominating vertices having the property that adding any new edge increases Kemeny's constant. We establish an analogous result for complete split graphs. We also prove that if a complete multipartite graph has enough dominating vertices, then there is always a non-edge whose addition will decrease Kemeny's constant.

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