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  • Hardness and tractability of detecting connected communities

    Author(s)
    Estivill-Castro, V
    Parsa, M
    Griffith University Author(s)
    Estivill-Castro, Vladimir
    Year published
    2016
    Metadata
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    Abstract
    We say that there is a community structure in a graph when the nodes of the graph can be partitioned into groups (communities) such that each group is internally more densely connected than with the rest of the graph. However, the challenge seems to specify what is to be dense, and what is relatively more connected (there seems to exist a similar situation to what is a cluster in unsupervised learning). Recently, Olsen [13] provided a general definition that is significantly more generic that others. We make two observations regarding such definition. First, we show that finding a community structure with k connected equal ...
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    We say that there is a community structure in a graph when the nodes of the graph can be partitioned into groups (communities) such that each group is internally more densely connected than with the rest of the graph. However, the challenge seems to specify what is to be dense, and what is relatively more connected (there seems to exist a similar situation to what is a cluster in unsupervised learning). Recently, Olsen [13] provided a general definition that is significantly more generic that others. We make two observations regarding such definition. First, we show that finding a community structure with k connected equal size communities is NP-complete. Then, we show that this problem can be solved efficiently on trees. Finally, we observed that every tree has a 2-community structure. This result is based on a reduction from an extremely popular heuristic (the Girvan-Neumann algorithm [12]) for detecting communities in large networks.
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    Conference Title
    ACM International Conference Proceeding Series
    Volume
    01-05-February-2016
    DOI
    https://doi.org/10.1145/2843043.2843053
    Subject
    Computational complexity and computability
    Data structures and algorithms
    Publication URI
    http://hdl.handle.net/10072/124180
    Collection
    • Conference outputs

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