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Fast Approximation Algorithms for Finding Node-Independent Paths in Networks


  • Douglas R. White
  • M. E. J. Newman


A network is robust to the extent that it is not vulnerable to disconnection by removal of nodes. The minimum number of nodes that need be removed to disconnect a pair of other nodes is called the connectivity of the pair. It can be proved that the connectivity is also equal to the number of node-independent paths between nodes, and hence we can quantify network robustness by calculating numbers of node-independent paths. Unfortunately, computing such numbers is known to be an NP-hard problem, taking exponentially long to run to completion. In this paper, we present an approximation algorithm which gives good lower bounds on numbers of node-independent paths between any pair of nodes on a directed or undirected graph in worst-case time which is linear in the graph size. A variant of the same algorithm can also calculate all the k-components of a graph in the same approximation. Our algorithm is found empirically to work with better than 99% accuracy on random graphs and for several real-world networks is 100% accurate. As a demonstration of the algorithm, we apply it to two large graphs for which the traditional NP-hard algorithm is entirely intractable--a network of collaborations between scientists and a network of business ties between biotechnology firms.

Suggested Citation

  • Douglas R. White & M. E. J. Newman, 2001. "Fast Approximation Algorithms for Finding Node-Independent Paths in Networks," Working Papers 01-07-035, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-07-035

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    References listed on IDEAS

    1. James G. March, 1991. "Exploration and Exploitation in Organizational Learning," Organization Science, INFORMS, vol. 2(1), pages 71-87, February.
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    Graph theory; social networks; cohesion; algorithms;

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