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Abstract
A proposed measure of network cohesion for graphs arising from interrelated economic
activity is studied. The measure is the largest singular value of a row-stochastic
matrix derived from the adjacency matrix. It is shown here that among graphs on
n
vertices, the star universally gives the (strictly) largest measure. Other universal
comparisons among graphs with larger measures are difficult to make, but one is
conjectured, and a selection of empirical evidence is given.
Keywords
graph singular values, graph measure, network cohesion
Mathematical Subject Classification 2010
Primary: 05C40, 15A18
Milestones
Received: 6 March 2013
Revised: 18 July 2013
Accepted: 24 July 2013
Published: 3 March 2015
Communicated by Joshua Cooper