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. 2012 Sep 27;7(9):e44459. doi: 10.1371/journal.pone.0044459

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© 2012 Liu 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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(a) A simple network of nodes. (b) The controlled network is represented by a directed graph with an input node connecting to a state node . The stem-cycle disjoint subgraph (shown in red) contains six edges, which is the largest number of edges among all possible stem-cycle disjoint subgraphs of the directed graph and corresponds to the generic dimension of controllable subspace by controlling node . The control centrality of node is thus . (c) The control centrality of the central hub in a directed star is always 2 for any network size . (d) The control centrality of a node in a directed acyclic graph (DAG) equals its layer index. In applying Hosoe’s theorem, if not all state nodes are accessible, we just need to consider the accessible part (highlighted in green) of the input node(s).

Inline graphic — (a) A simple network of nodes. (b) The controlled network is represented by a directed graph with an input node connecting to a state node . The stem-cycle disjoint subgraph (shown in red) contains six edges, which is the largest number of edges among all possible stem-cycle disjoint subgraphs of the directed graph and corresponds to the generic dimension of controllable subspace by controlling node . The control centrality of node is thus . (c) The control centrality of the central hub in a directed star is always 2 for any network size . (d) The control centrality of a node in a directed acyclic graph (DAG) equals its layer index. In applying Hosoe’s theorem, if not all state nodes are accessible, we just need to consider the accessible part (highlighted in green) of the input node(s).