Analysis of the Effect of Degree Correlation on the Size of Minimum Dominating Sets in Complex Networks

Abstract

Network controllability is an important topic in wide-ranging research fields. However, the relationship between controllability and network structure is poorly understood, although degree heterogeneity is known to determine the controllability. We focus on the size of a minimum dominating set (MDS), a measure of network controllability, and investigate the effect of degree-degree correlation, which is universally observed in real-world networks, on the size of an MDS. We show that disassortativity or negative degree-degree correlation reduces the size of an MDS using analytical treatments and numerical simulation, whereas positive correlations hardly affect the size of an MDS. This result suggests that disassortativity enhances network controllability. Furthermore, apart from the controllability issue, the developed techniques provide new ways of analyzing complex networks with degree-degree correlations.

Scientific Collaboration in a Multidisciplinary Organization Revealed by Network Science

“…Alternatively, it has been shown that scientific collaboration generally creates an assortative network [13,33]. Disassortative regimes have been acknowledged as an outcome of technological and biological networks [13] that embed some degree of controllability [20]. Therefore, Embrapa's scientific co-authorship network resembles networks with controls and constrains, which agrees with the findings by Zuo and Zhao [40] that more multidisciplinary institutions are not necessarily more collaborative.…”

“…It has been shown that the size of a minimum dominant set of a network, Γ, depends on µ, γ, and <k>, but not on modularity and clustering [19,20]. Decreases in Γ when µ ≤ 0 is due to the repulsion (competition) between hubs.…”

“…Furthermore, the degree correlation k nn (k) ∼ k , i.e., the tendency of nodes to connect to other nodes with similar (assortative, µ > 0) or dissimilar (disassortative, µ < 0) degrees, has been found assortative in many scientific collaboration networks [2,13]. On the other hand, it has been shown that scale-free networks can be controlled by a finite subset of the network, called the dominant set Γ (γ, µ, <k>) for which Γ ≤ n/2 [19,20].…”

Topology Universality and Dissimilarity in a Class of Scale-Free Networks

“…External control factors are expressed in many ways, such as determinacy [15], controllability [16] and stability [17]. Except that, researchers also put forward complexity [18, 19] and trade-off relationship [20] to study the topology characters for complex networks.…”

Effect of Correlations on Routing and Modeling of Time-varying Communication Networks

“…BA model assumes that a graph will evolve indefinitely without considering any constraint or limit on it.Apart from degree distribution, degree-degree correlation (DDC) is a network property in which nodes with similar attributes, such as degree, tend to be connected. The DDC has an important influence on the structural properties of the network and hence, used to measure stability, robustness [13], controllability of the network [14,15], spreading of diseases [16], the traffic dynamics on networks and other time varying processes. DDC is used to divide SF networks into three types: assortative, disassortative and neutral networks [17].…”