Target control and expandable target control of complex networks

Target control of complex networks, which aims to control only a target subset of network nodes instead of the entire network, is an outstanding challenge faced in various real world applications. Recently one fundamental issue regarding how to allocate a minimum number of control sources to guarantee the target controllability of a given target node set S was solved. This issue is shown to be essentially a path cover problem and it can be converted to a maximum network flow problem. In this work, we address another fundamental issue which is to further find the maximum (minimum) controllable node set to cover S using directed paths and circles based on the allocated minimum number of control sources. We show that such an issue can be solved by applying the maximum (minimum) cost maximum flow algorithm after introducing a cost for each edge in the flow network. Based on the obtained maximum (minimum) target controllable node set, we further propose a new index termed "expandable target controllability" to characterize complex networks that are expanding all the time. It is shown that "expandable target controllability" is an intrinsic property of various networks. We anticipate that this work would serve wide applications in target control and expandable target control of real-life networks. (C) 2019 Published by Elsevier Ltd on behalf of The Franklin Institute.