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Comparative evaluation of community detection algorithms: a topological approach

Community detection is one of the most active fields in complex network analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing the network structure in such cohesive subgroups to be revealed. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand index, normalized mutual information, etc). However, this type of comparison neglects the topological properties of the communities. In this paper, we present a comprehensive comparative study of a representative set of community detection methods, in which we adopt both types of evaluation. Community-oriented topological measures are used to qualify the communities and evaluate their deviation from the reference structure. In order to mimic real-world systems, we use artificially generated realistic networks. It turns out there is no equivalence between the two approaches: a high performance does not necessarily correspond to correct topological properties, and vice versa. They can therefore be considered as complementary, and we recommend applying both of them in order to perform a complete and accurate assessment.

A Comparison of Community Detection Algorithms on Artificial Networks

Community detection has become a very important part in complex networks analysis. Authors traditionally test their algorithms on a few real or artificial networks. Testing on real networks is necessary, but also limited: the considered real networks are usually small, the actual underlying communities are generally not defined objectively, and it is not possible to control their properties. Generating artificial networks makes it possible to overcome these limitations. Until recently though, most works used variations of the classic Erdős-Renyi random model and consequently suffered from the same flaws, generating networks not realistic enough. In this work, we use Lancichinetti et al. model, which is able to generate networks with controlled power-law degree and community distributions, to test some community detection algorithms. We analyze the properties of the generated networks and use the normalized mutual information measure to assess the quality of the results and compare the considered algorithms.

Qualitative Comparison of Community Detection Algorithms

Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on real-world and artificial networks, their performance being assessed through some partition similarity measure. However, artificial networks realism can be questioned, and the appropriateness of those measures is not obvious. In this study, we take advantage of recent advances concerning the characterization of community structures to tackle these questions. We first generate networks thanks to the most realistic model available to date. Their analysis reveals they display only some of the properties observed in real-world community structures. We then apply five community detection algorithms on these networks and find out the performance assessed quantitatively does not necessarily agree with a qualitative analysis of the identified communities. It therefore seems both approaches should be applied to perform a relevant comparison of the algorithms.

The Effect of Network Realism on Community Detection Algorithms

Community detection consists in searching cohesive subgroups in complex networks. It has recently become one of the domain pivotal questions for scientists in many different fields where networks are used as modeling tools. Algorithms performing community detection are usually tested on real, but also on artificial networks, the former being costly and difficult to obtain. In this context, being able to generate networks with realistic properties is crucial for the reliability of the tests. Recently, Lancichinetti et al. [1] designed a method to produce realistic networks, with a community structure and power law distributed degrees and community sizes. However, other realistic properties such as degree correlation and transitivity are missing. In this work, we propose a modification of their approach, based on the preferential attachment model, in order to remedy this limitation. We analyze the properties of the generated networks and compare them to the original approach. We then apply different community detection algorithms and observe significant changes in their performances when compared to results on networks generated with the original approach.

An Empirical Study of the Relation between Community Structure and Transitivity

One of the most prominent properties in real-world networks is the presence of a community structure, i.e. dense and loosely interconnected groups of nodes called communities. In an attempt to better understand this concept, we study the relationship between the strength of the community structure and the network transitivity (or clustering coefficient). Although intuitively appealing, this analysis was not performed before. We adopt an approach based on random models to empirically study how one property varies depending on the other. It turns out the transitivity increases with the community structure strength, and is also affected by the distribution of the community sizes. Furthermore, increasing the transitivity also results in a stronger community structure. More surprisingly, if a very weak community structure causes almost zero transitivity, the opposite is not true and a network with a close to zero transitivity can still have a clearly defined community structure. Further analytical work is necessary to characterize the exact nature of the identified relationship.

A method for characterizing communities in dynamic attributed complex networks

Many methods have been proposed to detect communities in complex networks, but very little work has been done regarding their interpretation. In this work, we propose an efficient method to tackle this problem. We first define a sequence-based representation of networks, combining temporal information, topological measures and nodal attributes. We then describe how to identify the most emerging sequential patterns of this dataset and use them to characterize the communities. We also show how to highlight outliers. Finally, as an illustration, we apply our method to a network of scientific collaborations.

Towards realistic artificial benchmark for community detection algorithms evaluation

Many algorithms have been proposed for revealing the community structure in complex networks. Tests under a wide range of realistic conditions must be performed in order to select the most appropriate for a particular application. Artificially generated networks are often used for this purpose. The most realistic generative method to date has been proposed by Lancichinetti, Fortunato and Radicchi LFR. However, it does not produce networks with some typical features of real-world networks. To overcome this drawback, we investigate two alternative modifications of this algorithm. Experimental results show that in both cases, centralisation and degree correlation values of generated networks are closer to those encountered in real-world networks. The three benchmarks have been used on a wide set of prominent community detection algorithms in order to reveal the limits and the robustness of the algorithms. Results show that the detection of meaningful communities gets harder with more realistic networks, and particularly when the proportion of inter-community links increases.

Interpreting communities based on the evolution of a dynamic attributed network

AbstractMany methods have been proposed to detect communities, not only in plain, but also in attributed, directed, or even dynamic complex networks. From the modeling point of view, to be of some utility, the community structure must be characterized relatively to the properties of the studied system. However, most of the existing works focus on the detection of communities, and only very few try to tackle this interpretation problem. Moreover, the existing approaches are limited either by the type of data they handle or by the nature of the results they output. In this work, we see the interpretation of communities as a problem independent from the detection process, consisting in identifying the most characteristic features of communities. We give a formal definition of this problem and propose a method to solve it. To this aim, we first define a sequence-based representation of networks, combining temporal information, community structure, topological measures, and nodal attributes. We then describe how to identify the most emerging sequential patterns of this dataset and use them to characterize the communities. We study the performance of our method on artificially generated dynamic attributed networks. We also empirically validate our framework on real-world systems: a DBLP network of scientific collaborations, and a LastFM network of social and musical interactions.

Exploring the Evolution of Node Neighborhoods in Dynamic Networks

Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of \textit{neighborhood event}, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes.

Overlapping Communities via k-Connected Ego Centered Groups

Overlapping community detection allows placing one node to multiple communities. Up to now, many algorithms are proposed for this issue. However, their accuracy depends on the overlapping level of the structure. In this work, we aim at finding relatively small overlapping communities independently than their overlapping level. We define k-connected node groups as cohesive groups in which each pair of nodes has at least k different node disjoint paths from one to another. We propose the algorithm EMOC first finding k-connected groups from the perspective of each node and second merging them to detect overlapping communities. We evaluate the accuracy of EMOC on artificial networks by comparing its results with foremost algorithms. The results indicate that EMOC can find small overlapping communities at any overlapping level. Results on real-world network show that EMOC finds relatively small but consistent communities.