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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
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Abstract |
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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 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
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Mathematical Subject Classification 2010
Primary: 05C40, 15A18
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Milestones
Received: 6 March 2013
Revised: 18 July 2013
Accepted: 24 July 2013
Published: 3 March 2015
Communicated by Joshua Cooper
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Authors |
| Charles R. Johnson | |
| Department of Mathematics College of William & Mary Williamsburg, VA 23187 United States |
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| Brian Lins | |
| Mathematics and Computer Science
Department Hampden-Sydney College Hampden Sydney, VA 23943 United States |
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| Victor Luo | |
| Department of Mathematics and
Statistics Williams College 2899 Paresky 39 Chapin Hall Drive Williamstown, MA 01267 United States |
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| Sean Meehan | |
| Department of Mathematics University of Notre Dame Notre Dame, IN 46556 United States |
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