Community Discovery is among the most studied problems in complex network analysis. During the last decade, many algorithms have been proposed to address such task; however, only a few of them have been integrated into a common framework, making it hard to use and compare different solutions. To support developers, researchers and practitioners, in this paper we introduce a python library - namely CDlib - designed to serve this need. The aim of CDlib is to allow easy and standardized access to a wide variety of network clustering algorithms, to evaluate and compare the results they provide, and to visualize them. It notably provides the largest available collection of community detection implementations, with a total of 39 algorithms.

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CDLIB : a python library to extract, compare and evaluate communities from complex networks

LGIEM: Global and local node influence based community detection

Identifying influential nodes in a network is a fundamental issue due to its wide applications, such as accelerating information diffusion or halting virus spreading. Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are made of groups of tightly connected nodes which are sparsely connected with the rest of the network in a so-called modular structure, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics of networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending on the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called “Modular centrality” is a two-dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. In order to illustrate the effectiveness of the Modular centrality extensions, comparison with their scalar counterparts is performed in an epidemic process setting. Simulation results using the Susceptible-Infected-Recovered (SIR) model on synthetic networks with controlled community structure allows getting a clear idea about the relation between the strength of the community structure and the major type of influence (global/local). Furthermore, experiments on real-world networks demonstrate the merit of this approach.

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Centrality in modular networks

Identifying influential spreaders in networks is an essential issue in order to prevent epidemic spreading, or to accelerate information diffusion. Several centrality measures take advantage of various network topological properties to quantify the notion of influence. However, the vast majority of works ignore its community structure while it is one of the main features of many real-world networks. In a recent study, we show that the centrality of a node in a network with non-overlapping communities depends on two features: Its local influence on the nodes belonging to its community, and its global influence on the nodes belonging to the other communities. Using global and local connectivity of the nodes, we introduced a framework allowing to redefine all the classical centrality measures (designed for networks without community structure) to non-overlapping modular networks. In this paper, we extend the so-called "Modular Centrality" to networks with overlapping communities. Indeed, it is a frequent scenario in real-world networks, especially for social networks where nodes usually belong to several communities. The "Overlapping Modular Centrality" is a two-dimensional measure that quantifies the local and global influence of overlapping and non-overlapping nodes. Extensive experiments have been performed on synthetic and real-world data using the Susceptible-Infected-Recovered (SIR) epidemic model. Results show that the Overlapping Modular Centrality outperforms its alternatives designed for non-modular networks. These investigations provide better knowledge on the influence of the various parameters governing the overlapping community structure on the nodes' centrality. Additionally, two combinations of the components of the Overlapping Modular Centrality are evaluated. Comparative analysis with competing methods shows that they produce more efficient centrality scores.

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Centrality in Complex Networks with Overlapping Community Structure.

Although community structure is ubiquitous in complex networks, few works exploit this topological property to control epidemics. In this work, devoted to networks with non-overlapping community structure (i.e., a node belongs to a single community), we propose and investigate three global immunization strategies. In order to characterize the influence of a node, various pieces of information are used such as the number of communities that the node can reach in one hop, the nature of the links (intra-community links, inter-community links), the size of the communities and the interconnection density between communities. Numerical simulations with the susceptible-infected-removed epidemiological model are conducted on both real-world and synthetic networks. Experimental results show that the proposed strategies are more effective than classical alternatives that are agnostic of the community structure. Additionally, they outperform alternative local and global strategies designed for modular networks.

https://hal.archives-ouvertes.fr/hal-02377044/document

Immunization of networks with non-overlapping community structure

Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment of these algorithms is a thriving open question. If the ground-truth community structure is available, various clustering-based metrics are used in order to compare it versus the one discovered by these algorithms. However, these metrics defined at the node level are fairly insensitive to the variation of the overall community structure. To overcome these limitations, we propose to exploit the topological features of the ‘community graphs’ (where the nodes are the communities and the links represent their interactions) in order to evaluate the algorithms. To illustrate our methodology, we conduct a comprehensive analysis of overlapping community detection algorithms using a set of real-world networks with known a priori community structure. Results provide a better perception of their relative performance as compared to classical metrics. Moreover, they show that more emphasis should be put on the topology of the community structure. We also investigate the relationship between the topological properties of the community structure and the alternative evaluation measures (quality metrics and clustering metrics). It appears clearly that they present different views of the community structure and that they must be combined in order to evaluate the effectiveness of community detection algorithms.

Community detection algorithm evaluation with ground-truth data

YouTube is the largest video-sharing social network where users (aka channels) can create links to any other users. Moreover, initially, users were allowed to create and join special groups of interest. Therefore, two types of online social networks can be defined. First, a user network where the nodes represent the users and the edges represent the social ties (friendship) between users. Second, a group network where the nodes represent the groups and the edges represent the social ties between groups, due to shared users. As the group network can be apprehended as the ground-truth overlapping community graph (where the nodes are the discovered communities and the links represent the overlap between the communities) of the user network, it is of prime interest to analyze and compare their topological structure. In this paper, we report the results of an extensive comparative evaluation of various macroscopic topological properties of both networks based on data from over one million users. Additionally, the community structure of the networks are uncovered using an overlapping community detection algorithm and the relationship between their community structure is investigated. The results of this study allow a better understanding of the relations between the mesoscopic and the macroscopic properties of online social networks, both from a topological and a functional point of view.

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User and group networks on YouTube: A comparative analysis

Community structure is one of the key properties of real-world complex networks. It plays a crucial role in their behaviors and topology. While an important work has been done on the issue of community detection, very little attention has been devoted to the analysis of the community structure. In this paper, we present an extensive investigation of the overlapping community network deduced from a large-scale co-authorship network. The nodes of the overlapping community network rep-resent the functional communities of the co-authorship network, and the links account for the fact that communities share some nodes in the co-authorship network. The comparative evaluation of the topological properties of these two networks shows that they share similar topological properties. These results are very interesting. Indeed, the network of communities seems to be a good representative of the original co-authorship network. With its smaller size, it may be more practical in order to realize various analyses that cannot be performed easily in large-scale real-world networks.

https://hal.archives-ouvertes.fr/hal-01534503/document

Overlapping Community Structure in Co-authorship Networks: A Case Study

Objective evaluation of community detection algorithms is a strategic issue. Indeed, we need to verify that the communities identified are actually the good ones. Moreover, it is necessary to compare results between two distinct algorithms to determine which is most effective. Classically, validations rely on clustering comparison measures or on quality metrics. Although, various traditional performance measures are used extensively. It appears very clearly that they cannot distinguish community structures with different topological properties. It is therefore necessary to propose an alternative methodology more sensitive to the community structure variations in order to conduct more effective comparisons. In this paper, we present a framework to tackle this challenge through a comprehensive analysis of the community structure of overlapping community structured networks. We illustrate our approach with an experimental analysis of a real-world network with a ground-truth community structure that we compare with the output of eight different overlapping community detection procedures, representative of categories of popular algorithms available in the literature. The results allow a better understanding of their behavior. Furthermore, they demonstrate that more emphasis should be put on the topology of the uncovered community structure in order to evaluate the effectiveness of community detection algorithms.

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Overlapping Community Detection Versus Ground-Truth in AMAZON Co-Purchasing Network

NURBS (Non-uniform rational B-splines) has become the industry standard tools for the representation, design and data exchange of geometric information to be processed and used by computers because of their useful geometrical properties. The problem of the parameterization of data points in NURBS curve/surface has been considered by several of researchers. We propose in this paper a new parameterization method for NURBS approximation. The current methods of parameterization such as centripetal method uses only the previous knot vector to calculate the recent knot. In this paper, we give a new parameterization method based on the correlation of the nodes. This approach inherits the advantages of the relation and position of the knots.

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Malek Jebabli

Papers

Community detection algorithm evaluation with ground-truth data

User and group networks on YouTube: A comparative analysis

Overlapping Community Structure in Co-authorship Networks: A Case Study

Overlapping Community Detection Versus Ground-Truth in AMAZON Co-Purchasing Network

NURBS parameterization: a new method of parameterization using the correlation relationship between nodes