Abstract
Many studies use community detection algorithms in order to understand complex networks. Most papers study node communities, i.e. groups of nodes, which may or may not overlap. A widely used measure to evaluate the quality of a community structure is the modularity. However, sometimes it is also relevant to study link partitions rather than node partitions. In order to evaluate a link partition, we propose a new quality function: Expected Nodes. Our function is based on the same inspiration as the modularity and compares, for a given link group, the number of incident nodes to the expected one. In this short note, we discuss the advantages and drawbacks of our quality function compared to other ones on synthetics graphs. We show that Expected Nodes is able to pass some fundamental sanity criteria and is the one that best identifies the most relevant partition in a more realistic context.
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Ahn, Y.-Y., Bagrow, J.P., Lehmann, S.: Link communities reveal multiscale complexity in networks. Nature 466(7307), 761–764 (2010)
Bender, E.A., Canfield, E.: The asymptotic number of labeled graphs with given degree sequences. Journal of Combinatorial Theory, Series A 24(3), 296–307 (1978)
Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008(10), P10008 (2008)
Evans, T.S., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 80(1), 016105 (2009)
Kim, S.: Community Detection in Directed Networks and its Application to Analysis of Social Networks. PhD thesis, Ohio State University (2014)
Kim, Y., Jeong, H.: Map equation for link communities. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 84(2), 026110 (2011)
Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 80, 016118 (2009)
Lim, S., Ryu, S., Kwon, S., Jung, K., Lee, J.-G.: LinkSCAN*: Overlapping community detection using the link-space transformation. In: 2014 IEEE 30th International Conference on Data Engineering, pp. 292–303. IEEE (March 2014)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 69 (2004)
Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences of the United States of America 105(4), 1118–1123 (2008)
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Gaumont, N., Queyroi, F., Magnien, C., Latapy, M. (2015). Expected Nodes: A Quality Function for the Detection of Link Communities. In: Mangioni, G., Simini, F., Uzzo, S., Wang, D. (eds) Complex Networks VI. Studies in Computational Intelligence, vol 597. Springer, Cham. https://doi.org/10.1007/978-3-319-16112-9_6
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DOI: https://doi.org/10.1007/978-3-319-16112-9_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16111-2
Online ISBN: 978-3-319-16112-9
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