Application of graph-spectral methods in the vulnerability assessment of water supply networks

We introduce a methodology based on spectral measurements of graph theory to establish the relative importance of areas in water supply networks (WSNs). To achieve an efficient vulnerability analysis, we have made a prospective study to establish the importance of areas based on two popular ranking algorithms — PageRank and HITS. These areas are analysed using a flexible method of semi-supervised clustering. This approach enables better control because it works top–down from the whole network to the detail of a particular area; and provides valuable additional support for assessing vulnerability in WSNs.

[1]  M. Cavers.  THE NORMALIZED LAPLACIAN MATRIX AND GENERAL RANDI C INDEX OF GRAPHS , 2010 .

[2]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[3]  Taher H. Haveliwala,et al.  The Second Eigenvalue of the Google Matrix , 2003 .

[4]  Carl D. Meyer,et al.  Deeper Inside PageRank , 2004, Internet Math..

[5]  Paul Jeffrey,et al.  A complex network approach to robustness and vulnerability of spatially organized water distribution networks , 2010, ArXiv.

[6]  Antonio Manuel,et al.  Improving water network management by efficient division into supply clusters , 2011 .

[7]  Idel Montalvo,et al.  Sensitivity analysis to assess the relative importance of pipes in water distribution networks , 2008, Math. Comput. Model..

[8]  Alan T. Murray,et al.  Comparative Approaches for Assessing Network Vulnerability , 2008 .

[9]  Joaquín Izquierdo,et al.  An approach to water supply clusters by semi-supervised learning , 2010 .

[10]  David Michaud,et al.  Methodology for Ranking the Elements of Water-Supply Networks , 2006 .

[11]  Kurt Bryan,et al.  The $25,000,000,000 Eigenvector: The Linear Algebra behind Google , 2006, SIAM Rev..

[12]  F. Pedroche,et al.  MÉTODOS DE CÁLCULO DEL VECTOR PAGERANK , 2008 .

[13]  M. Newman.  Random Graphs as Models of Networks , 2002, cond-mat/0202208.

[14]  Jon Kleinberg,et al.  Authoritative sources in a hyperlinked environment , 1999, SODA '98.

[15]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .