Abstract
Myriad problems can be described in hypergraph terms. However, the theory and tools are not sufficiently developed to allow most problems to be tackled directly within this context. The main purpose of this paper is to increase the awareness of this important gap and to encourage the development of this formal theory, in conjunction with the consideration of concrete applications. As a starting point, we concentrate on the problem of finding (small) subhypergraphs in a (large) hypergraph. Many existing algorithms reduce this problem to the known territory of graph theory by considering the 2-section graph. We argue that this is not the right approach, neither from a theoretical point of view (by considering a generalization of the classic model of binomial random graphs to hypergraphs) nor from a practical one (by performing experiments on two datasets).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alexander, M., Robins, G.: Small worlds among interlocking directors: network structures and distance in bipartite graphs. Comput. Math. Org. Theor. 10(1), 69–94 (2004)
Bahmanian, M., Sajna, M.: Connection, separation in hypergraphs (2015). arXiv:1504.04274v1
Bollobás, B.: Random Graphs. Cambridge University Press, Cambridge (2001)
Bollobás, B.: Random graphs. In: Temperley, H.N.V. (ed.) Combinatorics. London Mathematical Society Lecture Note Series, vol. 52, pp. 80–102. Cambridge University Press, Cambridge (1981)
Borgatti, S., Everett, M.: Network analysis of 2-mode data. Soc. Netw. 19(3), 243–269 (1997)
Duchet, P.: Hypergraphs. In: Graham, R.L., Grötschel, M., Lovász, L. (eds.) Handbook of Combinatorics. Elsevier, Amsterdam (1995)
Dudek, A., Frieze, A.M.: Loose Hamilton cycles in random \(k\)-uniform hypergraphs. Electron. J. Comb. 17, P48 (2011)
Dudek, A., Frieze, A.M.: Tight Hamilton cycles in random uniform hypergraphs. Random Struct. Algorithms 42, 374–385 (2012)
Ferber, A.: Closing gaps in problems related to Hamilton cycles in random graphs and hypergraphs (preprint)
Frieze, A.M., Karoński, M.: Introduction to Random Graphs. Cambridge University Press, Cambridge (2015)
Le Blond, S., Guillaume, J.-L., Latapy, M.: Clustering in P2P exchanges and consequences on performances. In: Castro, M., Renesse, R. (eds.) IPTPS 2005. LNCS, vol. 3640, pp. 193–204. Springer, Heidelberg (2005). doi:10.1007/11558989_18
Janson, S., Łuczak, T., Ruciński, A.: Random Graphs. Wiley, New York (2000)
Johansson, A., Kahn, J., Vu, V.: Factor in random graphs. Random Struct. Algorithms 33, 1–28 (2008)
Latapy, M., Magnien, C., Del Vecchio, N.: Basic notions for the analysis of large two-mode networks. Soc. Netw. 30(1), 31–48 (2008)
Zhou, W., Nakhleh, L.: Properties of metabolic graphs: biological organization or representation artifacts? BMC Bioinform. 12, 132 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Dewar, M. et al. (2016). Subgraphs in Non-uniform Random Hypergraphs. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2016. Lecture Notes in Computer Science(), vol 10088. Springer, Cham. https://doi.org/10.1007/978-3-319-49787-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-49787-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49786-0
Online ISBN: 978-3-319-49787-7
eBook Packages: Computer ScienceComputer Science (R0)