Abstract
Many complex systems exist in the physical world and therefore can be modeled by networks in which their nodes and edges are embedded in space. However, classical network motifs only use purely topological information and disregard other features. In this paper we introduce a novel and general subgraph abstraction that incorporates spatial information, therefore enriching its characterization power. Moreover, we describe and implement a method to compute and count our spatial subgraphs in any given network. We also provide initial experimental results by using our methodology to produce spatial fingerprints of real road networks, showcasing its discrimination power and how it captures more than just simple topology.
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- 1.
We will make available a github link to the source code if the paper is accepted.
References
Barthélemy, M.: Spatial networks. Phys. Rep. 499(1–3), 1–101 (2011)
Barthelemy, M.: Morphogenesis of spatial networks. Springer (2018)
Boguñá, M., Krioukov, D., Almagro, P., Serrano, M.Á.: Small worlds and clustering in spatial networks. Phys. Rev. Res. 2(2), 023040 (2020)
Choobdar, S., Ribeiro, P., Silva, F.: Motif mining in weighted networks. In: 2012 IEEE 12th International Conference on Data Mining Workshops, pp. 210–217. IEEE (2012)
Grohe, M., Schweitzer, P.: The graph isomorphism problem. Commun. ACM 63(11), 128–134 (2020)
Haklay, M., Weber, P.: Openstreetmap: user-generated street maps. IEEE Pervasive Comput. 7(4), 12–18 (2008)
Hasan, S., Schneider, C.M., Ukkusuri, S.V., González, M.C.: Spatiotemporal patterns of urban human mobility. J. Stat. Phys. 151(1), 304–318 (2013)
McKay, B.D., Piperno, A.: Practical graph isomorphism, ii. J. Symbol. Comput. 60, 94–112 (2014)
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)
Narizuka, T., Yamamoto, K., Yamazaki, Y.: Statistical properties of position-dependent ball-passing networks in football games. Phys. A Stat. Mech. Appl. 412, 157–168 (2014)
Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Paranjape, A., Benson, A.R., Leskovec, J.: Motifs in temporal networks. In: Proceedings of the tenth ACM International Conference on Web Search and Data Mining, pp. 601–610 (2017)
Pržulj, N.: Biological network comparison using graphlet degree distribution. Bioinformatics 23(2), e177–e183 (2007)
Ribeiro, P., Paredes, P., Silva, M.E., Aparicio, D., Silva, F.: A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets. ACM Comput. Surv. (CSUR) 54(2), 1–36 (2021)
Ribeiro, P., Silva, F.: Discovering colored network motifs. In: Complex Networks V, pp. 107–118. Springer (2014)
Sallmen, S., Nurmi, T., Kivelä, M.: Graphlets in multilayer networks. J. Complex Netw. 10(2), cnac005 (2022)
Wernicke, S.: Efficient detection of network motifs. IEEE/ACM Trans. Comput. Biol. Bioinform. 3(4), 347–359 (2006)
Acknowledgements
This work is partially financed financed by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia within project LA/P/0063/2020 and grant SFRH/BD/136525/2018. We would also like to thank the reviewers for the insightful comments.
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Ferreira, J., Barbosa, A., Ribeiro, P. (2023). Towards the Concept of Spatial Network Motifs. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_44
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DOI: https://doi.org/10.1007/978-3-031-21131-7_44
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