Structural Controllability of Complex Networks Based on Preferential Matching

Zhang, Xizhe; Lv, Tianyang; Yang, Xueying; Bin, Zhang

doi:10.1371/journal.pone.0112039

Cited by 23 publications

(15 citation statements)

References 39 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The driver nodes are known to avoids hubs which are essential to maintain network integrity [5]. Different algorithms, with varying complexity, have been proposed for finding maximal matching in a network [6–10]. Among them Hopcroft-Karp has the maximum flexibility and least complexity [7].…”

Section: Introductionmentioning

confidence: 99%

Control of Neuronal Network in Caenorhabditis elegans

Badhwar

Bagler

2015

PLoS ONE

View full text Add to dashboard Cite

Caenorhabditis elegans, a soil dwelling nematode, is evolutionarily rudimentary and contains only ∼ 300 neurons which are connected to each other via chemical synapses and gap junctions. This structural connectivity can be perceived as nodes and edges of a graph. Controlling complex networked systems (such as nervous system) has been an area of excitement for mankind. Various methods have been developed to identify specific brain regions, which when controlled by external input can lead to achievement of control over the state of the system. But in case of neuronal connectivity network the properties of neurons identified as driver nodes is of much importance because nervous system can produce a variety of states (behaviour of the animal). Hence to gain insight on the type of control achieved in nervous system we implemented the notion of structural control from graph theory to C. elegans neuronal network. We identified ‘driver neurons’ which can provide full control over the network. We studied phenotypic properties of these neurons which are referred to as ‘phenoframe’ as well as the ‘genoframe’ which represents their genetic correlates. We find that the driver neurons are primarily motor neurons located in the ventral nerve cord and contribute to biological reproduction of the animal. Identification of driver neurons and its characterization adds a new dimension in controllability of C. elegans neuronal network. This study suggests the importance of driver neurons and their utility to control the behaviour of the organism.

show abstract

Section: Introductionmentioning

confidence: 99%

Control of Neuronal Network in Caenorhabditis elegans

Badhwar

Bagler

2015

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…It paves the way to analyze the properties of all MIS s of a network, such as enumerate all MIS s14, estimate the node capacity in MIS s10 or find the optimum MIS under different control constraints or with specific node property21. Furthermore, the structural properties of the input graph, such as the node’s degree and connected component also reveal several important topics on controllability of a network.…”

Section: Discussionmentioning

confidence: 99%

“…A few works analyzed the node types in control1213 and control capacities10 of input nodes. Moreover, although any of its MIS s are capable of fully controlling the network, they may composed of nodes with different topological properties, such as high-degree nodes14. The existence of physical constraints and limitations15 may also affect the choice of a suitable MIS .…”

mentioning

confidence: 99%

Input graph: the hidden geometry in controlling complex networks

Zhang

2016

Sci Rep

Self Cite

View full text Add to dashboard Cite

The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder: what is the underlying relationship of all possible input nodes? Here we introduce input graph, a simple geometry that reveals the complex relationship between all control schemes and input nodes. We prove that the node adjacent to an input node in the input graph will appear in another control scheme, and the connected nodes in input graph have the same type in control, which they are either all possible input nodes or not. Furthermore, we find that the giant components emerge in the input graphs of many real networks, which provides a clear topological explanation of bifurcation phenomenon emerging in dense networks and promotes us to design an efficient method to alter the node type in control. The findings provide an insight into control principles of complex networks and offer a general mechanism to design a suitable control scheme for different purposes.Controlling complex networked systems is a fundamental challenge in natural, social sciences and engineered systems. A networked system is controllable if its state can be controlled from any initial state to a desired accessible state 1,2 by inputting external signals from a few suitable selected nodes, which are called input nodes 3-6 . Existing works 3 provide an efficient method based on maximum matching to find a Minimum Input nodes Set (abbreviated MIS) used to fully control a network.However, these works have primarily focused on analyzing single MIS 4-8 , while the underlying control relationships of nodes and MISs remain elusive. Owing to the structural complexity of a network, its MISs are typically not unique and the number of MISs are exponential to the size of the network 9,10 . The enumeration of all possible MISs is a #P problem 11 which requires high computational costs. A few works analyzed the node types in control 12,13 and control capacities 10 of input nodes. Moreover, although any of its MISs are capable of fully controlling the network, they may composed of nodes with different topological properties, such as high-degree nodes 14 . The existence of physical constraints and limitations 15 may also affect the choice of a suitable MIS. For example, when controlling an inter-bank market 16,17 , one may need certain specific input nodes to ensure that a MIS can be manipulated by a given organization; when controlling a protein interaction network 18 , some proteins cannot be used as input nodes because of technique limitation.Given the existence of numerous MISs in a network, a node can be classified based on its participation in MISs 12 : 1. possible input node, which appear in at least one MIS; 2. redundant node, which never appear in any MIS. Previous works 12 found that the dense networks exhibit a surprising bifurcation phenomenon, in which the majority of nodes are either redundant nodes or possibl...

show abstract

“…To obtain the expected input nodes of each bipartite graph, we use the preferential matching [15] to find maximum matching of each bipartite graph. The preferential matching method arranges the matching order of the nodes based on a predefined queue, and ensure that the nodes in the rear of the queue have a high probability of being input nodes.…”

Section: Methodsmentioning

confidence: 99%

Efficient target control of complex networks based on preferential matching

Zhang

Wang

2017

PLoS ONE

Self Cite

View full text Add to dashboard Cite

Controlling a complex network towards a desired state is of great importance in many applications. Existing works present an approximate algorithm to find the input nodes used to control partial nodes of the network. However, the input nodes obtained by this algorithm depend on the node matching order and cannot achieve optimum results. Here we present a novel algorithm to find the input nodes for target control based on preferential matching. The algorithm elaborately arranges the matching order of the nodes to reduce the size of the input node set. The results on both synthetic and real networks indicate that the proposed algorithm outperforms the previous algorithm.

show abstract

Structural Controllability of Complex Networks Based on Preferential Matching

Cited by 23 publications

References 39 publications

Control of Neuronal Network in Caenorhabditis elegans

Control of Neuronal Network in Caenorhabditis elegans

Input graph: the hidden geometry in controlling complex networks

Efficient target control of complex networks based on preferential matching

Contact Info

Product

Resources

About