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. 2014 Feb 26;9(2):e89066. doi: 10.1371/journal.pone.0089066

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© 2014 Nie et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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The network with size and , the green nodes are matched nodes and the red ones are unmatched. The purple edges are matching edges in maximum matching. However, the unmatched nodes , are the driver nodes which should be controlled directly by the inputs and , and after the edges failure, the unmatched nodes , , should be controlled by inputs , and . The red and green circles symbol the unmatched nodes and matched nodes, respectively. The purple lines symbol edges in maximum matching, and the dash lines symbol the failed edges in cascades. The red arrows symbol the input signals. The process of a,b,c,d shows the change of controllability in cascading failure.

Inline graphic — The network with size and , the green nodes are matched nodes and the red ones are unmatched. The purple edges are matching edges in maximum matching. However, the unmatched nodes , are the driver nodes which should be controlled directly by the inputs and , and after the edges failure, the unmatched nodes , , should be controlled by inputs , and . The red and green circles symbol the unmatched nodes and matched nodes, respectively. The purple lines symbol edges in maximum matching, and the dash lines symbol the failed edges in cascades. The red arrows symbol the input signals. The process of a,b,c,d shows the change of controllability in cascading failure.