19,350 research outputs found
Community detection by using the extended modularity
This article is about community detection algorithms in graphs. First a new method will be introduced, which is based on an extension [16] of the commonly used modularity [17, 18, 19, 20] and gives overlapping communities. We list and compare the results given by our new method and some other algorithms yielding either overlapping or non-overlapping communities. While the main use of the proposed algorithm is benchmarking, we also consider the possibility of hot starts, and some further extensions that considers the degree distribution of the graphs
Link Clustering with Extended Link Similarity and EQ Evaluation Division.
Link Clustering (LC) is a relatively new method for detecting overlapping communities in networks. The basic principle of LC is to derive a transform matrix whose elements are composed of the link similarity of neighbor links based on the Jaccard distance calculation; then it applies hierarchical clustering to the transform matrix and uses a measure of partition density on the resulting dendrogram to determine the cut level for best community detection. However, the original link clustering method does not consider the link similarity of non-neighbor links, and the partition density tends to divide the communities into many small communities. In this paper, an Extended Link Clustering method (ELC) for overlapping community detection is proposed. The improved method employs a new link similarity, Extended Link Similarity (ELS), to produce a denser transform matrix, and uses the maximum value of EQ (an extended measure of quality of modularity) as a means to optimally cut the dendrogram for better partitioning of the original network space. Since ELS uses more link information, the resulting transform matrix provides a superior basis for clustering and analysis. Further, using the EQ value to find the best level for the hierarchical clustering dendrogram division, we obtain communities that are more sensible and reasonable than the ones obtained by the partition density evaluation. Experimentation on five real-world networks and artificially-generated networks shows that the ELC method achieves higher EQ and In-group Proportion (IGP) values. Additionally, communities are more realistic than those generated by either of the original LC method or the classical CPM method
Node-Centric Detection of Overlapping Communities in Social Networks
We present NECTAR, a community detection algorithm that generalizes Louvain
method's local search heuristic for overlapping community structures. NECTAR
chooses dynamically which objective function to optimize based on the network
on which it is invoked. Our experimental evaluation on both synthetic benchmark
graphs and real-world networks, based on ground-truth communities, shows that
NECTAR provides excellent results as compared with state of the art community
detection algorithms
Extension of Modularity Density for Overlapping Community Structure
Modularity is widely used to effectively measure the strength of the disjoint
community structure found by community detection algorithms. Although several
overlapping extensions of modularity were proposed to measure the quality of
overlapping community structure, there is lack of systematic comparison of
different extensions. To fill this gap, we overview overlapping extensions of
modularity to select the best. In addition, we extend the Modularity Density
metric to enable its usage for overlapping communities. The experimental
results on four real networks using overlapping extensions of modularity,
overlapping modularity density, and six other community quality metrics show
that the best results are obtained when the product of the belonging
coefficients of two nodes is used as the belonging function. Moreover, our
experiments indicate that overlapping modularity density is a better measure of
the quality of overlapping community structure than other metrics considered.Comment: 8 pages in Advances in Social Networks Analysis and Mining (ASONAM),
2014 IEEE/ACM International Conference o
Additive Approximation Algorithms for Modularity Maximization
The modularity is a quality function in community detection, which was
introduced by Newman and Girvan (2004). Community detection in graphs is now
often conducted through modularity maximization: given an undirected graph
, we are asked to find a partition of that maximizes
the modularity. Although numerous algorithms have been developed to date, most
of them have no theoretical approximation guarantee. Recently, to overcome this
issue, the design of modularity maximization algorithms with provable
approximation guarantees has attracted significant attention in the computer
science community.
In this study, we further investigate the approximability of modularity
maximization. More specifically, we propose a polynomial-time
-additive approximation algorithm for the
modularity maximization problem. Note here that
holds. This improves the current best additive approximation error of ,
which was recently provided by Dinh, Li, and Thai (2015). Interestingly, our
analysis also demonstrates that the proposed algorithm obtains a nearly-optimal
solution for any instance with a very high modularity value. Moreover, we
propose a polynomial-time -additive approximation algorithm for the
maximum modularity cut problem. It should be noted that this is the first
non-trivial approximability result for the problem. Finally, we demonstrate
that our approximation algorithm can be extended to some related problems.Comment: 23 pages, 4 figure
Clustering and Community Detection in Directed Networks: A Survey
Networks (or graphs) appear as dominant structures in diverse domains,
including sociology, biology, neuroscience and computer science. In most of the
aforementioned cases graphs are directed - in the sense that there is
directionality on the edges, making the semantics of the edges non symmetric.
An interesting feature that real networks present is the clustering or
community structure property, under which the graph topology is organized into
modules commonly called communities or clusters. The essence here is that nodes
of the same community are highly similar while on the contrary, nodes across
communities present low similarity. Revealing the underlying community
structure of directed complex networks has become a crucial and
interdisciplinary topic with a plethora of applications. Therefore, naturally
there is a recent wealth of research production in the area of mining directed
graphs - with clustering being the primary method and tool for community
detection and evaluation. The goal of this paper is to offer an in-depth review
of the methods presented so far for clustering directed networks along with the
relevant necessary methodological background and also related applications. The
survey commences by offering a concise review of the fundamental concepts and
methodological base on which graph clustering algorithms capitalize on. Then we
present the relevant work along two orthogonal classifications. The first one
is mostly concerned with the methodological principles of the clustering
algorithms, while the second one approaches the methods from the viewpoint
regarding the properties of a good cluster in a directed network. Further, we
present methods and metrics for evaluating graph clustering results,
demonstrate interesting application domains and provide promising future
research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear
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