Resistance Distance, Information Centrality, Node Vulnerability and Vibrations in Complex Networks

Detecting Overlapping Communities with MDS and Local Expansion FCM

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.3295 ◽

2014 ◽

Vol 644-650 ◽

pp. 3295-3299

Author(s):

Lin Li ◽

Zheng Min Xia ◽

Sheng Hong Li ◽

Li Pan ◽

Zhi Hua Huang

Keyword(s):

Community Structure ◽

Euclidean Space ◽

Complex Networks ◽

Test Results ◽

Distance Information ◽

Overlapping Communities ◽

Expansion Strategy ◽

Local Expansion ◽

Structural And Functional Properties ◽

Overlapping Community

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.

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Improving Information Centrality of a Node in Complex Networks by Adding Edges

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/491 ◽

2018 ◽

Author(s):

Liren Shan ◽

Yuhao Yi ◽

Zhongzhi Zhang

Keyword(s):

Complex Networks ◽

Objective Function ◽

Optimization Problem ◽

Network Node ◽

Resistance Distance ◽

Running Time ◽

Practical Applications ◽

Approximation Factor ◽

Speed Up ◽

Effectiveness And Efficiency

The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality Iv of a given node v in a network with n nodes and m edges, by creating k new edges incident to v. Since Iv is the reciprocal of the sum of resistance distance Rv between v and all nodes, we alternatively consider the problem of minimizing Rv by adding k new edges linked to v. We show that the objective function is monotone and supermodular. We provide a simple greedy algorithm with an approximation factor (1 − 1/e) and O(n^3) running time. To speed up the computation, we also present an algorithm to compute (1 − 1/e − epsilon) approximate resistance distance Rv after iteratively adding k edges, the running time of which is Otilde(mk*epsilon^−2) for any epsilon > 0, where the Otilde(·) notation suppresses the poly(log n) factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.

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The Kirchhoff Index of Hypercubes and Related Complex Networks

Discrete Dynamics in Nature and Society ◽

10.1155/2013/543189 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 10

Author(s):

Jiabao Liu ◽

Jinde Cao ◽

Xiang-Feng Pan ◽

Ahmed Elaiw

Keyword(s):

Graph Theory ◽

Complex Networks ◽

Laplacian Matrix ◽

Exact Formula ◽

Spectral Graph Theory ◽

Kirchhoff Index ◽

Resistance Distance ◽

Spectral Graph ◽

Relationship Of ◽

The Relationship

The resistance distance between any two vertices ofGis defined as the network effective resistance between them if each edge ofGis replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices inG. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networksQnby utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networksQnand its three variant networksl(Qn),s(Qn),t(Qn)by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes ofl(Qn),s(Qn), andt(Qn)were proposed, respectively.

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Spectra, Hitting Times and Resistance Distances of q- Subdivision Graphs

The Computer Journal ◽

10.1093/comjnl/bxz141 ◽

2019 ◽

Author(s):

Yibo Zeng ◽

Zhongzhi Zhang

Keyword(s):

Complex Networks ◽

Hitting Times ◽

Kirchhoff Index ◽

Resistance Distance ◽

Scale Free ◽

Subdivision Graph ◽

Model Complex ◽

Hierarchical Lattices ◽

Simple Connected Graph ◽

Corona Product

Abstract Subdivision, triangulation, Kronecker product, corona product and many other graph operations or products play an important role in complex networks. In this paper, we study the properties of $q$-subdivision graphs, which have been applied to model complex networks. For a simple connected graph $G$, its $q$-subdivision graph $S_q(G)$ is obtained from $G$ through replacing every edge $uv$ in $G$ by $q$ disjoint paths of length 2, with each path having $u$ and $v$ as its ends. We derive explicit formulas for many quantities of $S_q(G)$ in terms of those corresponding to $G$, including the eigenvalues and eigenvectors of normalized adjacency matrix, two-node hitting time, Kemeny constant, two-node resistance distance, Kirchhoff index, additive degree-Kirchhoff index and multiplicative degree-Kirchhoff index. We also study the properties of the iterated $q$-subdivision graphs, based on which we obtain the closed-form expressions for a family of hierarchical lattices, which has been used to describe scale-free fractal networks.

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