2,362 research outputs found
Approximate Closest Community Search in Networks
Recently, there has been significant interest in the study of the community
search problem in social and information networks: given one or more query
nodes, find densely connected communities containing the query nodes. However,
most existing studies do not address the "free rider" issue, that is, nodes far
away from query nodes and irrelevant to them are included in the detected
community. Some state-of-the-art models have attempted to address this issue,
but not only are their formulated problems NP-hard, they do not admit any
approximations without restrictive assumptions, which may not always hold in
practice.
In this paper, given an undirected graph G and a set of query nodes Q, we
study community search using the k-truss based community model. We formulate
our problem of finding a closest truss community (CTC), as finding a connected
k-truss subgraph with the largest k that contains Q, and has the minimum
diameter among such subgraphs. We prove this problem is NP-hard. Furthermore,
it is NP-hard to approximate the problem within a factor , for
any . However, we develop a greedy algorithmic framework,
which first finds a CTC containing Q, and then iteratively removes the furthest
nodes from Q, from the graph. The method achieves 2-approximation to the
optimal solution. To further improve the efficiency, we make use of a compact
truss index and develop efficient algorithms for k-truss identification and
maintenance as nodes get eliminated. In addition, using bulk deletion
optimization and local exploration strategies, we propose two more efficient
algorithms. One of them trades some approximation quality for efficiency while
the other is a very efficient heuristic. Extensive experiments on 6 real-world
networks show the effectiveness and efficiency of our community model and
search algorithms
Motif Clustering and Overlapping Clustering for Social Network Analysis
Motivated by applications in social network community analysis, we introduce
a new clustering paradigm termed motif clustering. Unlike classical clustering,
motif clustering aims to minimize the number of clustering errors associated
with both edges and certain higher order graph structures (motifs) that
represent "atomic units" of social organizations. Our contributions are
two-fold: We first introduce motif correlation clustering, in which the goal is
to agnostically partition the vertices of a weighted complete graph so that
certain predetermined "important" social subgraphs mostly lie within the same
cluster, while "less relevant" social subgraphs are allowed to lie across
clusters. We then proceed to introduce the notion of motif covers, in which the
goal is to cover the vertices of motifs via the smallest number of (near)
cliques in the graph. Motif cover algorithms provide a natural solution for
overlapping clustering and they also play an important role in latent feature
inference of networks. For both motif correlation clustering and its extension
introduced via the covering problem, we provide hardness results, algorithmic
solutions and community detection results for two well-studied social networks
A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem
Many graph mining applications rely on detecting subgraphs which are
near-cliques. There exists a dichotomy between the results in the existing work
related to this problem: on the one hand the densest subgraph problem (DSP)
which maximizes the average degree over all subgraphs is solvable in polynomial
time but for many networks fails to find subgraphs which are near-cliques. On
the other hand, formulations that are geared towards finding near-cliques are
NP-hard and frequently inapproximable due to connections with the Maximum
Clique problem.
In this work, we propose a formulation which combines the best of both
worlds: it is solvable in polynomial time and finds near-cliques when the DSP
fails. Surprisingly, our formulation is a simple variation of the DSP.
Specifically, we define the triangle densest subgraph problem (TDSP): given
, find a subset of vertices such that , where is the number of triangles induced
by the set . We provide various exact and approximation algorithms which the
solve the TDSP efficiently. Furthermore, we show how our algorithms adapt to
the more general problem of maximizing the -clique average density. Finally,
we provide empirical evidence that the TDSP should be used whenever the output
of the DSP fails to output a near-clique.Comment: 42 page
A Unified Community Detection, Visualization and Analysis method
Community detection in social graphs has attracted researchers' interest for
a long time. With the widespread of social networks on the Internet it has
recently become an important research domain. Most contributions focus upon the
definition of algorithms for optimizing the so-called modularity function. In
the first place interest was limited to unipartite graph inputs and partitioned
community outputs. Recently bipartite graphs, directed graphs and overlapping
communities have been investigated. Few contributions embrace at the same time
the three types of nodes. In this paper we present a method which unifies
commmunity detection for the three types of nodes and at the same time merges
partitionned and overlapping communities. Moreover results are visualized in
such a way that they can be analyzed and semantically interpreted. For
validation we experiment this method on well known simple benchmarks. It is
then applied to real data in three cases. In two examples of photos sets with
tagged people we reveal social networks. A second type of application is of
particularly interest. After applying our method to Human Brain Tractography
Data provided by a team of neurologists, we produce clusters of white fibers in
accordance with other well known clustering methods. Moreover our approach for
visualizing overlapping clusters allows better understanding of the results by
the neurologist team. These last results open up the possibility of applying
community detection methods in other domains such as data analysis with
original enhanced performances.Comment: Submitted to Advances in Complex System
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