38,253 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
The topology of a discussion: the #occupy case
We analyse a large sample of the Twitter activity developed around the social
movement 'Occupy Wall Street' to study the complex interactions between the
human communication activity and the semantic content of a discussion. We use a
network approach based on the analysis of the bipartite graph @Users-#Hashtags
and of its projections: the 'semantic network', whose nodes are hashtags, and
the 'users interest network', whose nodes are users In the first instance, we
find out that discussion topics (#hashtags) present a high heterogeneity, with
the distinct role of the communication hubs where most the 'opinion traffic'
passes through. In the second case, the self-organization process of users
activity leads to the emergence of two classes of communicators: the
'professionals' and the 'amateurs'. Moreover the network presents a strong
community structure, based on the differentiation of the semantic topics, and a
high level of structural robustness when a certain set of topics are censored
and/or accounts are removed. Analysing the characteristics the @Users-#Hashtags
network we can distinguish three phases of the discussion about the movement.
Each phase corresponds to specific moment of the movement: from declaration of
intent, organisation and development and the final phase of political
reactions. Each phase is characterised by the presence of specific #hashtags in
the discussion. Keywords: Twitter, Network analysisComment: 13 pages, 9 figure
On Spectral Graph Embedding: A Non-Backtracking Perspective and Graph Approximation
Graph embedding has been proven to be efficient and effective in facilitating
graph analysis. In this paper, we present a novel spectral framework called
NOn-Backtracking Embedding (NOBE), which offers a new perspective that
organizes graph data at a deep level by tracking the flow traversing on the
edges with backtracking prohibited. Further, by analyzing the non-backtracking
process, a technique called graph approximation is devised, which provides a
channel to transform the spectral decomposition on an edge-to-edge matrix to
that on a node-to-node matrix. Theoretical guarantees are provided by bounding
the difference between the corresponding eigenvalues of the original graph and
its graph approximation. Extensive experiments conducted on various real-world
networks demonstrate the efficacy of our methods on both macroscopic and
microscopic levels, including clustering and structural hole spanner detection.Comment: SDM 2018 (Full version including all proofs
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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