Controlling edge dynamics in complex networks

By Tamás Nepusz, Tamás Vicsek. Nature Physics, 2011

429 citations recorded by the source corpus.

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the past decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics. Surprisingly little is known about how network dynamics might be controlled, despite extensive research into how they behave. A study of the controllability of network edge dynamics reveals that it differs from that of nodal dynamics, and that real-world networks are easier to control than their random counterparts.

Subfields: Computer Networks and Communications, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8ec887cc0bdbd8389012125969f3acbc58169f34

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Citations in the corpus

Control Centrality and Hierarchical Structure in Complex Networks (2012, background): “While these principles have significantly enriched our understanding of many networks that affect our lives, our ultimate goal is to develop the capability to control them [5–17].”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “…analytic analysis that the clustering coefficient and the community structure (modularity) have no significant impact on the minimum number of driver nodes ND. Interestingly, degree correlations demonstrate a robust effect on controllability, which manifest the findings in Nepusz and Vicsek (2012).”
Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review (2012, methodology): “…complex network hierarchy measures (Cornelius et al., 2011; Liu et al., 2011, 2012; Banerjee & Roy, 2012; Cowan et al., 2012; Mones et al., 2012; Nepusz & Vicsek, 2012; Wang et al., 2012a; Yazicioglu et al., 2012) may uncover multiple target sets, as shown by the assessment of the…”
Target control of complex networks (2014, positive): “By mapping the structural controllability problem 13 to a maximum matching problem 14 , we were able to identify a minimum set of driver nodes of size N D , sufﬁcient to control the whole network 12,15 .”
Minimal Controllability Problems (2013, neutral): “trollability properties of networks [2], [3], [5], [9], [10], [12], [13]–[16], [21], [24], [27], [29], [34]–[36], [38] with similar”
Exact controllability of complex networks (2013, background): “The structural-controllability framework also allows several basic issues to be addressed, such as linear edge dynamics [38], lower and upper bounds of energy required for control [39], control centrality [40], and optimization [41].”
On Submodularity and Controllability in Complex Dynamical Networks (2014, background): “Many other studies of controllability in complex networks have followed, including [37], [31], [45], [47], [43].”
Control Principles of Complex Networks (2015, methodology): “For example, driver nodes prefer hubs with large out-degree and heterogeneous networks are more controllable, i.e., require fewer driver nodes, than homogeneous networks (Nepusz and Vicsek, 2012).”