Vol. 8, No. 2, 2015

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Ordering graphs in a normalized singular value measure

Charles R. Johnson, Brian Lins, Victor Luo and Sean Meehan

Vol. 8 (2015), No. 2, 263–273

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.

graph singular values, graph measure, network cohesion
Mathematical Subject Classification 2010
Primary: 05C40, 15A18
Received: 6 March 2013
Revised: 18 July 2013
Accepted: 24 July 2013
Published: 3 March 2015

Communicated by Joshua Cooper
Charles R. Johnson
Department of Mathematics
College of William & Mary
Williamsburg, VA 23187
United States
Brian Lins
Mathematics and Computer Science Department
Hampden-Sydney College
Hampden Sydney, VA 23943
United States
Victor Luo
Department of Mathematics and Statistics
Williams College
2899 Paresky
39 Chapin Hall Drive
Williamstown, MA 01267
United States
Sean Meehan
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
United States