Detection of local community structures in complex dynamic networks with random walks

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

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Generalized Dissipative State Estimation of Singularly Perturbed Switched Complex Dynamic Networks With Persistent Dwell-Time Mechanism

IEEE Transactions on Systems Man and Cybernetics Systems ◽

10.1109/tsmc.2020.3034635 ◽

2020 ◽

pp. 1-12

Author(s):

Hao Shen ◽

Xiaohui Hu ◽

Xuangou Wu ◽

Shuping He ◽

Jing Wang

Keyword(s):

State Estimation ◽

Dwell Time ◽

Dynamic Networks ◽

Singularly Perturbed ◽

Complex Dynamic ◽

Dissipative State

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Finite-Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

Complexity ◽

10.1155/2019/9821063 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Yiping Luo ◽

Yuejie Yao

Keyword(s):

Finite Time ◽

Time Synchronization ◽

Dynamic Networks ◽

Nonlinear Function ◽

Time Instant ◽

Control Input ◽

Parameter Uncertainties ◽

Complex Dynamic ◽

Network Nodes ◽

Analysis Techniques

The finite-time synchronization control is studied in this paper for a class of nonlinear uncertain complex dynamic networks. The uncertainties in the network are unknown but bounded and satisfy some matching conditions. The coupling relationship between network nodes is described by a nonlinear function satisfying the Lipchitz condition. By introducing a simple Lyapunov function, two main results regarding finite-time synchronization of a class of complex dynamic networks with parameter uncertainties are derived. By employing some analysis techniques like matrix inequalities, suitable controllers can be designed based on the obtained synchronization criteria. Moreover, with the obtained control input, the time instant required for the system to achieve finite-time synchronization can be estimated if a set of LMIs are feasible or an assumption on the eigenvalues of some matrices can be satisfied. Finally, the effectiveness of the proposed results is verified by numerical simulation.

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Random Walks, Interacting Particles, Dynamic Networks: Randomness Can Be Helpful

Structural Information and Communication Complexity - Lecture Notes in Computer Science ◽

10.1007/978-3-642-22212-2_1 ◽

2011 ◽

pp. 1-14 ◽

Cited By ~ 6

Author(s):

Colin Cooper

Keyword(s):

Random Walks ◽

Dynamic Networks ◽

Interacting Particles

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Identifying influential nodes in dynamic social networks based on degree-corrected stochastic block model

International Journal of Modern Physics B ◽

10.1142/s0217979216500922 ◽

2016 ◽

Vol 30 (16) ◽

pp. 1650092 ◽

Cited By ~ 5

Author(s):

Tingting Wang ◽

Weidi Dai ◽

Pengfei Jiao ◽

Wenjun Wang

Keyword(s):

Social Networks ◽

Real World ◽

Dynamic Networks ◽

Dynamic Network ◽

Community Structures ◽

Block Model ◽

Real World Data ◽

Stochastic Block Model ◽

Dynamic Social Networks ◽

Influential Nodes

Many real-world data can be represented as dynamic networks which are the evolutionary networks with timestamps. Analyzing dynamic attributes is important to understanding the structures and functions of these complex networks. Especially, studying the influential nodes is significant to exploring and analyzing networks. In this paper, we propose a method to identify influential nodes in dynamic social networks based on identifying such nodes in the temporal communities which make up the dynamic networks. Firstly, we detect the community structures of all the snapshot networks based on the degree-corrected stochastic block model (DCBM). After getting the community structures, we capture the evolution of every community in the dynamic network by the extended Jaccard’s coefficient which is defined to map communities among all the snapshot networks. Then we obtain the initial influential nodes of the dynamic network and aggregate them based on three widely used centrality metrics. Experiments on real-world and synthetic datasets demonstrate that our method can identify influential nodes in dynamic networks accurately, at the same time, we also find some interesting phenomena and conclusions for those that have been validated in complex network or social science.

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