Abstract
Densely connected parts in networks are referred to as “communities”. Community structure is a hallmark of a variety of real-world networks; individual communities form functional modules constituting complex systems described by networks. Therefore, revealing community structure in networks is essential to approaching and understanding complex systems described by networks. This is the reason why network science has made a great deal of effort to develop effective and efficient methods for detecting communities in networks. Here we examine a novel type of community detection, which has not been examined so far but will be of great practical use. Suppose that we are given a set of source nodes that includes some (but not all) of “true” members of a particular community; suppose also that the set includes some nodes that are not the members of this community (i.e., “false” members of the community). We propose to detect the community from this “imperfect” and “inaccurate” set of source nodes using attractor neural-network dynamics. Community detection achieved by the proposed method can be viewed as restoration of the original pattern from a deteriorated pattern, which is also analogous to cue-triggered recall of short-term memory in the brain. We demonstrate the effectiveness of the proposed method using synthetic networks and real social networks for which correct communities are known.
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This study was partly supported by KAKENHI (15K00418).
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Appendix: Synthetic Benchmark Network
Appendix: Synthetic Benchmark Network
The benchmark network used in Sect. 3.1 was synthesized using the software downloaded from [15] under the following settings: Number of nodes 1000; average degree 15; maximum degree 50; exponent for the degree distribution 2; exponent for the community size distribution 1; mixing parameter 0.2; minimum for the community sizes 20; maximum for the community sizes 50. The synthesized network has 30 communities, with the following size occurrences: (size, occurrence) = (20, 1), (21, 2), (23, 1), (26, 4), (27, 2), (28, 2), (29, 1), (30, 1), (31, 2), (33, 1), (34, 1), (36, 1), (37, 1), (38, 1), (40, 1), (41, 3), (42, 1), (44, 2), (471, 1), (62, 1).
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Okamoto, H. (2015). Community Detection as Pattern Restoration by Attractor Neural-Network Dynamics. In: Lones, M., Tyrrell, A., Smith, S., Fogel, G. (eds) Information Processing in Cells and Tissues. IPCAT 2015. Lecture Notes in Computer Science(), vol 9303. Springer, Cham. https://doi.org/10.1007/978-3-319-23108-2_17
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DOI: https://doi.org/10.1007/978-3-319-23108-2_17
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