761 research outputs found
On the Permanence of Vertices in Network Communities
Despite the prevalence of community detection algorithms, relatively less
work has been done on understanding whether a network is indeed modular and how
resilient the community structure is under perturbations. To address this
issue, we propose a new vertex-based metric called "permanence", that can
quantitatively give an estimate of the community-like structure of the network.
The central idea of permanence is based on the observation that the strength
of membership of a vertex to a community depends upon the following two
factors: (i) the distribution of external connectivity of the vertex to
individual communities and not the total external connectivity, and (ii) the
strength of its internal connectivity and not just the total internal edges.
In this paper, we demonstrate that compared to other metrics, permanence
provides (i) a more accurate estimate of a derived community structure to the
ground-truth community and (ii) is more sensitive to perturbations in the
network. As a by-product of this study, we have also developed a community
detection algorithm based on maximizing permanence. For a modular network
structure, the results of our algorithm match well with ground-truth
communities.Comment: 10 pages, 5 figures, 8 tables, Accepted in 20th ACM SIGKDD Conference
on Knowledge Discovery and Data Minin
Detecting Stable Communities In Large Scale Networks
A network is said to exhibit community structure if the nodes of the network can be easily grouped into groups of nodes, such that each group is densely connected internally but sparsely connected with other groups. Most real world networks exhibit community structure.
A popular technique for detecting communities is based on computing the modularity of the network. Modularity reflects how well the vertices in a group are connected as opposed to being randomly connected. We propose a parallel algorithm for detecting modularity in large networks.
However, all modularity based algorithms for detecting community structure are affected by the order in which the vertices in the network are processed. Therefore, detecting communities in real world graphs becomes increasingly difficult. We introduce the concept of stable community, that is, a group of vertices that are always partitioned to the same community independent of the vertex perturbations to the input. We develop a preprocessing step that identifies stable communities and empirically show that the number of stable communities in a network affects the range of modularity values obtained. In particular, stable communities can also help determine strong communities in the network.
Modularity is a widely accepted metric for measuring the quality of a partition identified by various community detection algorithms. However, a growing number of researchers have started to explore the limitations of modularity maximization such as resolution limit, degeneracy of solutions and asymptotic growth of the modularity value for detecting communities. In order to address these issues we propose a novel vertex-level metric called permanence. We show that our metric permanence as compared to other standard metrics such as modularity, conductance and cut-ratio performs as a better community scoring function for evaluating the detected community structures from both synthetic networks and real-world networks. We demonstarte that maximizing permanence results in communities that match the ground-truth structure of networks more accurately than modularity based and other approaches. Finally, we demonstrate how maximizing permanence overcomes limitations associated with modularity maximization
Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities
The rock-paper-scissor game -- which is characterized by three strategies
R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and
R excludes S -- serves as a simple prototype for studying more complex
non-transitive systems. For well-mixed systems where interactions result in
fitness reductions of the losers exceeding fitness gains of the winners,
classical theory predicts that two strategies go extinct. The effects of
spatial heterogeneity and dispersal rates on this outcome are analyzed using a
general framework for evolutionary games in patchy landscapes. The analysis
reveals that coexistence is determined by the rates at which dominant
strategies invade a landscape occupied by the subordinate strategy (e.g. rock
invades a landscape occupied by scissors) and the rates at which subordinate
strategies get excluded in a landscape occupied by the dominant strategy (e.g.
scissor gets excluded in a landscape occupied by rock). These invasion and
exclusion rates correspond to eigenvalues of the linearized dynamics near
single strategy equilibria. Coexistence occurs when the product of the invasion
rates exceeds the product of the exclusion rates. Provided there is sufficient
spatial variation in payoffs, the analysis identifies a critical dispersal rate
required for regional persistence. For dispersal rates below , the
product of the invasion rates exceed the product of the exclusion rates and the
rock-paper-scissor metacommunities persist regionally despite being extinction
prone locally. For dispersal rates above , the product of the exclusion
rates exceed the product of the invasion rates and the strategies are
extinction prone. These results highlight the delicate interplay between
spatial heterogeneity and dispersal in mediating long-term outcomes for
evolutionary games.Comment: 31pages, 5 figure
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