3,938 research outputs found
Balanced Butterfly Counting in Bipartite-Network
Bipartite graphs offer a powerful framework for modeling complex
relationships between two distinct types of vertices, incorporating
probabilistic, temporal, and rating-based information. While the research
community has extensively explored various types of bipartite relationships,
there has been a notable gap in studying Signed Bipartite Graphs, which capture
liking / disliking interactions in real-world networks such as
customer-rating-product and senator-vote-bill. Balance butterflies,
representing 2 x 2 bicliques, provide crucial insights into antagonistic
groups, balance theory, and fraud detection by leveraging the signed
information. However, such applications require counting balance butterflies
which remains unexplored. In this paper, we propose a new problem: counting
balance butterflies in a signed bipartite graph. To address this problem, we
adopt state-of-the-art algorithms for butterfly counting, establishing a smart
baseline that reduces the time complexity for solving our specific problem. We
further introduce a novel bucket approach specifically designed to count
balanced butterflies efficiently. We propose a parallelized version of the
bucketing approach to enhance performance. Extensive experimental studies on
nine real-world datasets demonstrate that our proposed bucket-based algorithm
is up to 120x faster over the baseline, and the parallel implementation of the
bucket-based algorithm is up to 45x faster over the single core execution.
Moreover, a real-world case study showcases the practical application and
relevance of counting balanced butterflies
Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization
Most of the distributed protocols for multi-agent consensus assume that the
agents are mutually cooperative and "trustful," and so the couplings among the
agents bring the values of their states closer. Opinion dynamics in social
groups, however, require beyond these conventional models due to ubiquitous
competition and distrust between some pairs of agents, which are usually
characterized by repulsive couplings and may lead to clustering of the
opinions. A simple yet insightful model of opinion dynamics with both
attractive and repulsive couplings was proposed recently by C. Altafini, who
examined first-order consensus algorithms over static signed graphs. This
protocol establishes modulus consensus, where the opinions become the same in
modulus but may differ in signs. In this paper, we extend the modulus consensus
model to the case where the network topology is an arbitrary time-varying
signed graph and prove reaching modulus consensus under mild sufficient
conditions of uniform connectivity of the graph. For cut-balanced graphs, not
only sufficient, but also necessary conditions for modulus consensus are given.Comment: scheduled for publication in IEEE Transactions on Automatic Control,
2016, vol. 61, no. 7 (accepted in August 2015
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