Algebraic connectivity and graph robustness.

Technical Report · Wed Jul 01 04:00:00 EDT 2009

DOI:https://doi.org/10.2172/973665· OSTI ID:973665

Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T ^[1]

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1. University of New Mexico

Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 973665
• Report Number(s): SAND2009-4494
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
ALGEBRA
BOUNDARY CONDITIONS
Computer network protocols-Mathematical models.
Computer networks.
DIAGRAMS
EIGENVALUES
LAPLACIAN
NETWORK ANALYSIS
SECURITY