34,983 research outputs found
Measuring robustness of community structure in complex networks
The theory of community structure is a powerful tool for real networks, which
can simplify their topological and functional analysis considerably. However,
since community detection methods have random factors and real social networks
obtained from complex systems always contain error edges, evaluating the
robustness of community structure is an urgent and important task. In this
letter, we employ the critical threshold of resolution parameter in Hamiltonian
function, , to measure the robustness of a network. According to
spectral theory, a rigorous proof shows that the index we proposed is inversely
proportional to robustness of community structure. Furthermore, by utilizing
the co-evolution model, we provides a new efficient method for computing the
value of . The research can be applied to broad clustering problems
in network analysis and data mining due to its solid mathematical basis and
experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1303.7434 by other author
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
Multi-scale Modularity in Complex Networks
We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure
Defining and Evaluating Network Communities based on Ground-truth
Nodes in real-world networks organize into densely linked communities where
edges appear with high concentration among the members of the community.
Identifying such communities of nodes has proven to be a challenging task
mainly due to a plethora of definitions of a community, intractability of
algorithms, issues with evaluation and the lack of a reliable gold-standard
ground-truth.
In this paper we study a set of 230 large real-world social, collaboration
and information networks where nodes explicitly state their group memberships.
For example, in social networks nodes explicitly join various interest based
social groups. We use such groups to define a reliable and robust notion of
ground-truth communities. We then propose a methodology which allows us to
compare and quantitatively evaluate how different structural definitions of
network communities correspond to ground-truth communities. We choose 13
commonly used structural definitions of network communities and examine their
sensitivity, robustness and performance in identifying the ground-truth. We
show that the 13 structural definitions are heavily correlated and naturally
group into four classes. We find that two of these definitions, Conductance and
Triad-participation-ratio, consistently give the best performance in
identifying ground-truth communities. We also investigate a task of detecting
communities given a single seed node. We extend the local spectral clustering
algorithm into a heuristic parameter-free community detection method that
easily scales to networks with more than hundred million nodes. The proposed
method achieves 30% relative improvement over current local clustering methods.Comment: Proceedings of 2012 IEEE International Conference on Data Mining
(ICDM), 201
Performance of a community detection algorithm based on semidefinite programming
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block model or planted partition problem, where a phase transition takes place in the detection of the planted partition by changing the signal-to-noise ratio. Optimal algorithms for the detection exist which are based on spectral methods, but we show these are extremely sensible to slight modification in the generative model. Recently Javanmard, Montanari and Ricci-Tersenghi [1] have used statistical physics arguments, and numerical simulations to show that finding communities in the stochastic block model via semidefinite programming is quasi optimal. Further, the resulting semidefinite relaxation can be solved efficiently, and is very robust with respect to changes in the generative model. In this paper we study in detail several practical aspects of this new algorithm based on semidefinite programming for the detection of the planted partition. The algorithm turns out to be very fast, allowing the solution of problems with O(105) variables in few second on a laptop computer
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