scholarly journals About complexity of complex networks

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Alexander Goryashko ◽  
Leonid Samokhine ◽  
Pavel Bocharov

Abstract We derive complexity estimates for two classes of deterministic networks: the Boolean networks S(Bn, m), which compute the Boolean vector-functions Bn, m, and the classes of graphs $G(V_{P_{m,\,l}}, E)$ G ( V P m , l , E ) , with overlapping communities and high density. The latter objects are well suited for the synthesis of resilience networks. For the Boolean vector-functions, we propose a synthesis of networks on a NOT, AND, and OR logical basis and unreliable channels such that the computation of any Boolean vector-function is carried out with polynomial information cost.All vertexes of the graphs $G(V_{P_{m,\,l}}, E)$ G ( V P m , l , E ) are labeled by the trinomial (m2±l,m)-partitions from the set of partitions Pm, l. It turns out that such labeling makes it possible to create networks of optimal algorithmic complexity with highly predictable parameters. Numerical simulations of simple graphs for trinomial (m2±l,m)-partition families (m=3,4,…,9) allow for the exact estimation of all commonly known topological parameters for the graphs. In addition, a new topological parameter—overlapping index—is proposed. The estimation of this index offers an explanation for the maximal density value for the clique graphs $G(V_{P_{m,\,l}}, E)$ G ( V P m , l , E ) .

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Haipeng Peng ◽  
Lixiang Li ◽  
Jürgen Kurths ◽  
Shudong Li ◽  
Yixian Yang

Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.


2014 ◽  
Vol 644-650 ◽  
pp. 3295-3299
Author(s):  
Lin Li ◽  
Zheng Min Xia ◽  
Sheng Hong Li ◽  
Li Pan ◽  
Zhi Hua Huang

Community structure is an important feature to understand structural and functional properties in various complex networks. In this paper, we use Multidimensional Scaling (MDS) to map nodes of network into Euclidean space to keep the distance information of nodes, and then we use topology feature of communities to propose the local expansion strategy to detect initial seeds for FCM. Finally, the FCM are used to uncover overlapping communities in the complex networks. The test results in real-world and artificial networks show that the proposed algorithm is efficient and robust in uncovering overlapping community structure.


2015 ◽  
Vol 18 (07n08) ◽  
pp. 1550018 ◽  
Author(s):  
DINGJIE WANG ◽  
SUOQIN JIN ◽  
FANG-XIANG WU ◽  
XIUFEN ZOU

The controlling of complex networks is one of the most challenging problems in modern network science. Accordingly, the required energy cost of control is a fundamental and significant problem. In this paper, we present the theoretical analysis and numerical simulations to study the controllability of complex networks from the energy perspective. First, by combining theoretical derivation and numerical simulations, we obtain lower bounds of the maximal and minimal energy costs for an arbitrary normal network, which are related to the eigenvalues of the state transition matrix. Second, we deduce that controlling unstable normal networks is easier than controlling stable normal networks with the same size. Third, we demonstrate a tradeoff between the control energy and the average degree (or the maximum degree) of an arbitrary undirected network. Fourth, numerical simulations show that the energy cost is negatively correlated with the degree of nodes. Moreover, the combinations of control nodes with the greater sum of degree need less energy to implement complete control. Finally, we propose a multi-objective optimization model to obtain the control strategy, which not only ensures the fewer control nodes but also guarantees the less energy cost of control.


2015 ◽  
Vol 5 (5) ◽  
pp. 1099-1103 ◽  
Author(s):  
Madhusudan Paul ◽  
Rishav Anand ◽  
Ashish Anand

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengrong Xie ◽  
Yuhua Xu ◽  
Dongbing Tong

We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.


2010 ◽  
Vol 21 (06) ◽  
pp. 785-793 ◽  
Author(s):  
HAIFENG ZHANG ◽  
MING ZHAO ◽  
BINGHONG WANG

Most previous studies on the synchronization of complex networks were based on that each node managed to adjust its neighbors coupling strength to enhance synchronizability, i.e. each node tried to adjust its total input coupling strength in a proper way and the neighbor nodes were passively adjusted. From practical and engineering viewpoints, each node should manage to adjust its total output coupling strength to realize synchronization. Moreover, each node's total output coupling strength can be distributed to its neighbors with different proportions. In view of the above reasons, in this paper, we study the synchronization of complex networks under the assumptions that the total output coupling strength of each node is voluntarily/directly distributed to its neighbors with different proportions. What is more, we assume that the total output coupling strength of each node can be nonlinear to its degree. Our analysis and numerical simulations show that the synchronizability can be enhanced dramatically when the parameters are properly selected.


2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Zhengzhong Yuan ◽  
Jianping Cai ◽  
Meili Lin

Global synchronization in adaptive coupling networks is studied in this paper. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with different topologies.


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