A New Information-Theoretical Distance Measure for Evaluating Community Detection Algorithms

Community detection is a research area from network science dealing withthe investigation of complex networks such as social or biological networks, aimingto identify subgroups (communities) of entities (nodes) thatare more closely relatedto each other inside the community than with the remaining entities in the network.Various community detection algorithms have been developed and used in the literaturehowever evaluating community structures that have been automatically detected isa challenging task due to varying results in different scenarios.Current evaluationmeasures that compare extracted community structures with the reference structure orground truth suffer from various drawbacks; some of them having beenpoint out in theliterature. Information theoretic measures form a fundamental classin this domain andhave recently received increasing interest. However even the well employed measures(NVI and NID) also share some limitations, particularly they are biased toward thenumber of communities in the network. The main contribution ofthis paper is tointroduce a new measure that overcomes this limitation while holding the importantproperties of measures. We review the mathematical properties of our measure based on¿2divergence inspired fromf-divergence measures in information theory. Theoreticalproperties as well as experimental results in various scenarios show the superiority of theproposed measure to evaluate community detection over the ones from the literature

Network Community Detection on Metric Space

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings

Comparative Evaluation of Community Detection Algorithms: A Topological Approach

Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. 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 article, 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 both 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

Median evidential c-means algorithm and its application to community detection

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods