Hierarchical benchmark graphs for testing community detection algorithms (original) (raw)
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Benchmark graphs for testing community detection algorithms
Physical Review E, 2008
Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a new class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this new benchmark to test two popular methods of community detection, modularity optimization and Potts model clustering. The results show that the new benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.
Physical Review E, 2009
Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like social networks. As a practical application, we show how modularity optimization performs on our new benchmark.
Community detection algorithms: A comparative analysis
Physical Review E, 2009
Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.
ArXiv, 2020
Community detection is a fundamental problem in the analysis of complex networks. It is the analogue of clustering in network data mining. Within community detection methods, hierarchical algorithms are popular. However, their iterative nature and the need to recompute the structural properties used to split the network (i.e. edge betweenness in Girvan and Newman's algorithm), make them unsuitable for large network data sets. In this paper, we study how local structural network properties can be used as proxies to improve the efficiency of hierarchical community detection while, at the same time, achieving competitive results in terms of modularity. In particular, we study the potential use of the structural properties commonly used to perform local link prediction, a supervised learning problem where community structure is relevant, as nodes are prone to establish new links with other nodes within their communities. In addition, we check the performance impact of network prunin...
Qualitative Comparison of Community Detection Algorithms
2011
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 art of community detection
BioEssays, 2008
Networks in nature possess a remarkable amount of structure. Via a series of datadriven discoveries, the cutting edge of network science has recently progressed from positing that the random graphs of mathematical graph theory might accurately describe real networks to the current viewpoint that networks in nature are highly complex and structured entities. The identification of high order structures in networks unveils insights into their functional organization. Recently, Clauset, Moore, and Newman 1 , introduced a new algorithm that identifies such heterogeneities in complex networks by utilizing the hierarchy that necessarily organizes the many levels of structure. Here, we anchor their algorithm in a general community detection framework and discuss the future of community detection.
Detecting the overlapping and hierarchical community structure of complex networks
2009
Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results.
A Comparison of Community Detection Algorithms on Artificial Networks
2009
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-Rényi 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.
On Accuracy of Community Structure Discovery Algorithms
2011
Community structure discovery in complex networks is a quite challenging problem spanning many applications in various disciplines such as biology, social network and physics. Emerging from various approaches numerous algorithms have been proposed to tackle this problem. Nevertheless little attention has been devoted to compare their efficiency on realistic simulated data. To better understand their relative performances, we evaluate systematically eleven algorithms covering the main approaches. The Normalized Mutual Information (NMI) measure is used to assess the quality of the discovered community structure from controlled artificial networks with realistic topological properties. Results show that along with the network size, the average proportion of intra-community to inter-community links is the most influential parameter on performances. Overall, "Infomap" is the leading algorithm, followed by "Walktrap", "SpinGlass" and "Louvain" which also achieve good consistency.