Hardness and tractability of detecting connected communities

Vladimir Estivill-Castro, Mahdi Parsa

Research output: Chapter in Book/Report/Conference proceedingConference Paper published in Proceedingspeer-review

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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 GirvanNeumann algorithm [12]) for detecting communities in large networks.
Original languageEnglish
Title of host publicationProceedings of the Australasian Computer Science Week Multiconference
Place of PublicationUnited States of America
PublisherAssociation for Computing Machinery (ACM)
Number of pages6
ISBN (Print)978-1-4503-4042-7
Publication statusPublished - 2016
Externally publishedYes
EventAustralasian Computer Science Week (ACSW2016) - Canberra, Australia
Duration: 2 Feb 20165 Feb 2016


ConferenceAustralasian Computer Science Week (ACSW2016)
Abbreviated titleACSW
Internet address


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