1,032 research outputs found
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
Community Detection via Maximization of Modularity and Its Variants
In this paper, we first discuss the definition of modularity (Q) used as a
metric for community quality and then we review the modularity maximization
approaches which were used for community detection in the last decade. Then, we
discuss two opposite yet coexisting problems of modularity optimization: in
some cases, it tends to favor small communities over large ones while in
others, large communities over small ones (so called the resolution limit
problem). Next, we overview several community quality metrics proposed to solve
the resolution limit problem and discuss Modularity Density (Qds) which
simultaneously avoids the two problems of modularity. Finally, we introduce two
novel fine-tuned community detection algorithms that iteratively attempt to
improve the community quality measurements by splitting and merging the given
network community structure. The first of them, referred to as Fine-tuned Q, is
based on modularity (Q) while the second one is based on Modularity Density
(Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of
modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds
on four real networks, and also on the classical clique network and the LFR
benchmark networks, each of which is instantiated by a wide range of
parameters. The results indicate that Fine-tuned Qds is the most effective
among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can
be applied to the communities detected by other algorithms to significantly
improve their results
Parallel Toolkit for Measuring the Quality of Network Community Structure
Many networks display community structure which identifies groups of nodes
within which connections are denser than between them. Detecting and
characterizing such community structure, which is known as community detection,
is one of the fundamental issues in the study of network systems. It has
received a considerable attention in the last years. Numerous techniques have
been developed for both efficient and effective community detection. Among
them, the most efficient algorithm is the label propagation algorithm whose
computational complexity is O(|E|). Although it is linear in the number of
edges, the running time is still too long for very large networks, creating the
need for parallel community detection. Also, computing community quality
metrics for community structure is computationally expensive both with and
without ground truth. However, to date we are not aware of any effort to
introduce parallelism for this problem. In this paper, we provide a parallel
toolkit to calculate the values of such metrics. We evaluate the parallel
algorithms on both distributed memory machine and shared memory machine. The
experimental results show that they yield a significant performance gain over
sequential execution in terms of total running time, speedup, and efficiency.Comment: 8 pages; in Network Intelligence Conference (ENIC), 2014 Europea
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