Exact Signed Modularity Density Maximization Solutions and Their Real Meaning*

The rapid evolution of social networks in recent years has focused the attention of researchers to find adequate solutions for the management of these networks. For this purpose, several efficient algorithms dedicated to the tracking and the rapid detection of the community structure have been proposed. In this paper, we propose a novel density-based approach with dual optimization for tracking community structure of increasing social networks. These networks are part of dynamic networks evolving by adding nodes with their links. The local optimization of the density makes it possible to reduce the resolution limit problem generated by the optimization of the modularity. The presented algorithm is incremental with a relatively low algorithmic complexity, making it efficient and faster. To demonstrate the effectiveness of our method, we test it on social networks of the real world. The experimental results show the performance and efficiency of our algorithm measured in terms of modularity density, modularity, normalized mutual information, number of communities discovered, running time and stability of communities.

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Penguins Search Optimization Algorithm for Community Detection in Complex Networks

International Journal of Applied Metaheuristic Computing ◽

10.4018/ijamc.2018010101 ◽

2018 ◽

Vol 9 (1) ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Mohamed Guendouz ◽

Abdelmalek Amine ◽

Reda Mohamed Hamou

Keyword(s):

Social Networks ◽

Complex Networks ◽

Community Detection ◽

Optimization Algorithm ◽

Optimization Problem ◽

Search Optimization ◽

Density Evaluation ◽

Evaluation Measure ◽

Modularity Density ◽

Initialization Strategy

In the last decade, the problem of community detection in complex networks has attracted the attention of many researchers in many domains, several methods and algorithms have been proposed to deal with this problem, many of them consider it as an optimization problem and various bio-inspired algorithms have been applied to solve it. In this work, the authors propose a new method for community detection in complex networks using the Penguins Search Optimization Algorithm (PeSOA), the authors use the modularity density evaluation measure as a function to maximize and they propose also to enhance the algorithm by using a new initialization strategy. The proposed algorithm has been tested on four popular real-world networks; experimental results compared with other known algorithms show the effectiveness of using this method for community detection in social networks.

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Modularity density of network community divisions

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2009.03.015 ◽

2009 ◽

Vol 238 (14) ◽

pp. 1161-1167 ◽

Cited By ~ 4

Author(s):

Erik Holmström ◽

Nicolas Bock ◽

Johan Brännlund

Keyword(s):

Network Community ◽

Modularity Density

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Complete mixed integer linear programming formulations for modularity density based clustering

Discrete Optimization ◽

10.1016/j.disopt.2017.03.002 ◽

2017 ◽

Vol 25 ◽

pp. 141-158 ◽

Cited By ~ 2

Author(s):

Alberto Costa ◽

Tsan Sheng Ng ◽

Lin Xuan Foo

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Mixed Integer ◽

Density Based Clustering ◽

Modularity Density

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A ground truth contest between modularity maximization and modularity density maximization

Artificial Intelligence Review ◽

10.1007/s10462-019-09802-8 ◽

2020 ◽

Vol 53 (6) ◽

pp. 4575-4599

Author(s):

R. de Santiago ◽

Luís C. Lamb

Keyword(s):

Ground Truth ◽

Modularity Maximization ◽

Modularity Density

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A Discrete Black Hole Optimization Algorithm for Efficient Community Detection in Social Networks

Handbook of Research on Biomimicry in Information Retrieval and Knowledge Management - Advances in Web Technologies and Engineering ◽

10.4018/978-1-5225-3004-6.ch009 ◽

2018 ◽

pp. 133-153

Author(s):

Mohamed Guendouz

Keyword(s):

Social Networks ◽

Black Hole ◽

Community Detection ◽

Optimization Algorithm ◽

Np Hard Problem ◽

Density Evaluation ◽

Evaluation Measure ◽

Networks Analysis ◽

Modularity Density ◽

New Strategies

In recent years, social networks analysis has attracted the attention of many researchers. Community detection is one of the highly studied problems in this field. It is considered an NP-hard problem, and several algorithms have been proposed to solve this problem. In this chapter, the authors present a new algorithm for community detection in social networks based on the Black Hole optimization algorithm. The authors use the modularity density evaluation measure as a function to maximize. They also propose the enhancement of the algorithm by using two new strategies: initialization and evolution. The proposed algorithm has been tested on famous synthetic and real-world networks; experimental results compared with three known algorithms show the effectiveness of using this algorithm for community detection in social networks.

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Uncovering the effective interval of resolution parameter across multiple community optimization measures

International Journal of Modern Physics B ◽

10.1142/s0217979217500412 ◽

2017 ◽

Vol 31 (06) ◽

pp. 1750041

Author(s):

Hui-Jia Li ◽

Qing Cheng ◽

He-Jin Mao ◽

Huanian Wang ◽

Junhua Chen

Keyword(s):

Ad Hoc ◽

Hamiltonian Function ◽

Limit Problem ◽

Resolution Limit ◽

Resolution Parameter ◽

Discrete Convex Analysis ◽

Modularity Density ◽

Density Measure ◽

Discrete Convex ◽

Primary Focus

The study of community structure is a primary focus of network analysis, which has attracted a large amount of attention. In this paper, we focus on two famous functions, i.e., the Hamiltonian function [Formula: see text] and the modularity density measure [Formula: see text], and intend to uncover the effective thresholds of their corresponding resolution parameter [Formula: see text] without resolution limit problem. Two widely used example networks are employed, including the ring network of lumps as well as the ad hoc network. In these two networks, we use discrete convex analysis to study the interval of resolution parameter of [Formula: see text] and [Formula: see text] that will not cause the misidentification. By comparison, we find that in both examples, for Hamiltonian function [Formula: see text], the larger the value of resolution parameter [Formula: see text], the less resolution limit the network suffers; while for modularity density [Formula: see text], the less resolution limit the network suffers when we decrease the value of [Formula: see text]. Our framework is mathematically strict and efficient and can be applied in a lot of scientific fields.

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