Abstract
Recently, one type of mesoscale structure called core-periphery (CP) structure has received much attention in complex networks, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. The core-periphery structure refers to that core nodes are densely interconnected, while periphery nodes are connected to core nodes to different extents, and periphery nodes are sparsely interconnected. Core-periphery structure containing a single core or multiple cores has been identified in various networks. However, investigation of the detection problems of the core-periphery has not been summarized in the literature. In this paper, we first introduce the definition of the core-periphery structure. The core-periphery structure has been paid more and more attention by researchers in various fields since its introduction, and it has been proved to be a powerful tool to analyze the theory of various topologies in our society, we briefly expounded the application of core-periphery structure in economics, sociology, medicine and other fields, and revealed the huge development potential of this theory. Then, we give a detailed overview of classical detection algorithms since the core-periphery structure theory was proposed. Finally, we give the development characteristics and the possible research directions of the core-periphery detection algorithm.





Similar content being viewed by others
References
Ahn, Y.-Y., Bagrow, J.P., Lehmann, S.: Link communities reveal multiscale complexity in networks. Nature 466(7307), 761 (2010)
Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic block models. J. Mach. Learn. Res. 9, 1981–2014 (2008)
Alba, R.D., Moore, G.: Elite social circles. Soc. Methods Res. 7(2), 167–188 (1978)
Anastasiou, Dimitrios, Louri, Helen, Tsionas, Mike: Nonperforming loans in the euro area: a re core–periphery banking markets fragmented? Int. J. Finance Econ. 24(1), 97–112 (2019)
Bailin, A.: From traditional to Group Hegemony: the G7, the Liberal Economic Order and the Core-Periphery Gap. Routledge, Abingdon (2017)
Ball, Brian, Newman, Mark E.J.: Friendship networks and social status. Soc. Netw. 1(1), 16–30 (2013)
Bassett, D.S., Wymbs, N.F., Rombach, M.P., Porter, M.A., Mucha, P.J., Grafton, S.T.: Task-based core-periphery organization of human brain dynamics. PLoS Comput. Biol. 9(9), e1003171 (2013)
Battiston, F., Guillon, J., Chavez, M., Latora, V., DeVicoFallani, F.: Multiplex core–periphery organization of the human connectome. J. R. Soc. Interface 15(146), 20180514 (2018)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)
Borgatti, S.P., Everett, M.G.: Models of core/periphery structures. Soc. Netw. 21(4), 375–395 (2000)
Boyd, J.P., Fitzgerald, W.J., Mahutga, M.C., Smith, D.A.: Computing continuous core/periphery structures for social relations data with minres/svd. Soc. Netw. 32(2), 125–137 (2010)
Brassil, A., Nodari, G.: A Density-based estimator of core/periphery network structures: analysing the australian interbank market. No. rdp2018-01. Reserve Bank of Australia (2018)
Brusco, M.: An exact algorithm for a core/periphery bipartitioning problem. Soc. Netw. 33(1), 12–19 (2011)
Brusco, M.J., Cradit, J.D.: Graph coloring, minimum-diameter partitioning, and the analysis of confusion matrices. J. Math. Psychol. 48(5), 301–309 (2004)
Brusco, M.J., Stahl, S.: An interactive multiobjective programming approach to combinatorial data analysis. Psychometrika 66(1), 5–24 (2001)
Burt, R. B. R. S.: Networks of collective action: a perspective on community influence systems. by Edward O. Laumann; Franz U. Pappi. Contemp. Sociol. 7(2), 152–153 (1978)
Chen, T., Tang, L.-A., Sun, Y., Chen, Z., Chen, H., Jiang, G.: Integrating community and role detection in information networks. In: Proceedings of the 2016 SIAM International Conference on Data Mining, pp, 72–80. SIAM (2016)
Cheng, C.-H.: A branch and bound clustering algorithm. IEEE Trans. Syst. Man Cybern 25(5), 895–898 (1995)
Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98 (2008)
Copus, A.K.: From core-periphery to polycentric development: concepts of spatial and aspatial peripherality. Eur. Plan. Stud. 9(4), 539–552 (2001)
Craig, B., Von Peter, G.: Interbank tiering and money center banks. J. Finan. Intermed. 23(3), 322–347 (2014)
Csermely, P., London, A., Ling-Yun, W., Uzzi, B.: Structure and dynamics of core/periphery networks. J. Complex Netw. 1(2), 93–123 (2013)
Cucuringu, M., Rombach, P., Lee, S.H., Porter, M.A.: Detection of core–periphery structure in networks using spectral methods and geodesic paths. Eur. J. Appl. Math. 27(6), 846–887 (2016)
Da Silva, M.R., Ma, H., Zeng, A.-P.: Centrality, network capacity, and modularity as parameters to analyze the core-periphery structure in metabolic networks. Proc. IEEE 96(8), 1411–1420 (2008)
Decelle, A., Krzakala, F., Moore, C., Zdeborová, L.: Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Phys. Rev. E 84(6), 066106 (2011a)
Decelle, A., Krzakala, F., Moore, C., Zdeborová, L.: Inference and phase transitions in the detection of modules in sparse networks. Phys. Rev. Lett. 107(6), 065701 (2011b)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. J. R. Stat. Soc. Ser. B (Methodol.) 39(1), 1–22 (1977)
Doreian, P.: Structural equivalence in a psychology journal network. J. Am. Soc. Inf. Sci. 36(6), 411–417 (1985)
Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci 5(1), 17–60 (1960)
Everett, M.G., Borgatti, S.P.: Peripheries of cohesive subsets. Soc. Netw. 21(4), 397–407 (2000)
Fagiolo, G., Reyes, Javier, Schiavo, Stefano: The evolution of the world trade web: a weighted-network analysis. J. Evol. Econ. 20(4), 479–514 (2010)
Forslid, R., Ottaviano, G.I.P.: An analytically solvable core-periphery model. J. Econ. Geogr. 3(3), 229–240 (2003)
Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3–5), 75–174 (2010)
Fricke, D., Lux, T.: Core–periphery structure in the overnight money market: evidence from the e-mid trading platform. Comput. Econ. 45(3), 359–395 (2015)
Garas, A., Schweitzer, F., Havlin, S.: A k-shell decomposition method for weighted networks. New J. Phys. 14(8), 083030 (2012)
Girvan, Mi, Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)
Hansen, P., Delattre, M.: Complete-link cluster analysis by graph coloring. J. Am. Stat. Assoc. 73(362), 397–403 (1978)
Hidalgo, C.A., Klinger, B., Barabási, A.-L., Hausmann, R.: The product space conditions the development of nations. Science 317(5837), 482–487 (2007)
Holme, P.: Core-periphery organization of complex networks. Phys. Rev. E 72(4), 046111 (2005)
Hughes, D.W., Holland, D.W.: (Core-periphery economic linkages: a measure of spread and possible backwash effects for the. Land Econ., 70(3), 1994
Jeske, R.J.: World-systems theory, core-periphery interactions, and elite economic exchange in mississippian societies. World-Systems Theory in Practice: Leadership, Production, and Exchange, pp. 203–221 (1999)
Jia, J., Benson, A.R: Detecting core-periphery structure in spatial networks. arXiv preprint arXiv:1808.06544 (2018)
Karrer, B., Newman, M.E.J.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83(1), 016107 (2011)
Karwa, V., Pelsmajer, M.J., Petrović, S., Stasi, D., Wilburne, D., et al.: Statistical models for cores decomposition of an undirected random graph. Electron. J. Stat. 11(1), 1949–1982 (2017)
Klein, G., Aronson, J.E.: Optimal clustering: a model and method. Naval Res. Log. (NRL) 38(3), 447–461 (1991)
Kojaku, S., Masuda, N.: Finding multiple core-periphery pairs in networks. Phys. Rev. E 96(5), 052313 (2017)
Kojaku, S., Cimini, G.,Caldarelli, G., Masuda, N.: Structural changes in the interbank market across the financial crisis from multiple core-periphery analysis. arXiv preprint arXiv:1802.05139. (2018)
Krugman, P.: Increasing returns and economic geography. J. Polit. Econ. 99(3), 483–499 (1991)
Laumann, E.O., Pappi, F.U.: Networks of Collective Action: A Perspective on Community Influence Systems. Elsevier, Amsterdam (2013)
Lee, S.H., Cucuringu, M., Porter, M.A.: Density-based and transport-based core-periphery structures in networks. Phys. Rev. E 89(3), 032810 (2014)
Lu-An T., et al.: On discovery of traveling companions from streaming trajectories. In: 2012 IEEE 28th International Conference on Data Engineering. IEEE (2012)
Ma, C,, Xiang, B.-B., Zhang, H.-F., Chen, H.-S., Small M.: Detection of core-periphery structure in networks by 3-tuple motifs. arXiv preprint arXiv:1705.04062 (2017)
Malecki EJ.: Technology and economic development: the dynamics of local, regional, and national change. University of Illinois at Urbana-Champaign’s Academy for Entrepreneurial Leadership Historical Research Reference in Entrepreneurship. (1997)
Maslov, S., Sneppen, K.: Specificity and stability in topology of protein networks. Science 296(5569), 910–913 (2002)
Mullins, N. C., Hargens, L. L., Kick, H. E. L.: The group structure of cocitation clusters: a comparative study. Am. Sociol. Rev. 42(4), 552–562 (1977)
Nemeth, R.J., Smith, D.A.: International trade and world-system structure: a multiple network analysis. Review (Fernand Braudel Center) 8(4), 517–560 (1985)
Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74(3), 036104 (2006)
Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)
Noble, J.: General internal medicine in internal medicine: at the core or on the periphery. Ann. Intern. Med. 116(12_Part_2), 1058–1060 (1992)
Nocete, F., Sáez, R., Nieto, J.M., Cruz-Auñón, R., Cabrero, R., Alex, E., Bayona, M.R.: Circulation of silicified oolitic limestone blades in south-iberia (spain and portugal) during the third millennium bc: an expression of a core/periphery framework. J. Anthropol. Archaeol. 24(1), 62–81 (2005)
Nowicki, K., Snijders, T.A.B.: Estimation and prediction for stochastic blockstructures. J. Am. Stat. Assoc. 96(455), 1077–1087 (2001)
Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814 (2005)
Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Phys. Rev. E 67(2), 026112 (2003)
Rombach, M.P., Porter, M.A., Fowler, J.H., Mucha, P.J.: Core-periphery structure in networks. SIAM J. Appl. Math. 74(1), 167–190 (2014)
Rossa, F.D., Dercole, F., Piccardi, C.: Profiling core-periphery network structure by random walkers. Sci. Rep. 3, 1467 (2013)
Ruggera, R.A., Blendinger, P.G., Gomez, M.D., Marshak, C.: Linking structure and functionality in mutualistic networks: do core frugivores disperse more seeds than peripheral species? Oikos 125(4), 541–555 (2016)
Shanahan, M., Wildie, M.: Knotty-centrality: finding the connective core of a complex network. PLoS One 7(5), e36579 (2012)
Shneiderman, B., Plaisant, C.: Designing the User Interface: Strategies for Effective Human-Computer Interaction. Pearson Education India, New Delhi (2010)
Smith, D.A., White, D.R.: Structure and dynamics of the global economy: network analysis of international trade 1965–1980. Soc. Forces 70(4), 857–893 (1992)
Snyder, D., Kick, E.L.: Structural position in the world system and economic growth, 1955-1970: a multiple-network analysis of transnational interactions. Am. J. Sociol. 84(5), 1096–1126 (1979)
Steiber, S.R.: The world system and world trade: an empirical exploration of conceptual conflicts. Sociol. Q. 20(1), 23–36 (1979)
Szymanski, B.K., Yener, B. (eds.): Advances in Pervasive Computing and Networking. Springer Science & Business Media, Berlin (2006)
Tickner, A.B.: Core, periphery and (neo) imperialist international relations. Eur. J. Int. Relat. 19(3), 627–646 (2013)
Tudisco, F., Higham, D.J.: A nonlinear spectral method for core-periphery detection in networks. SIAM J. Math. Data Sci. 1(2), 269–292 (2019)
Verma, T., Russmann, F., Araújo, N.A.M., Nagler, J., Herrmann, H.J.: Emergence of core–peripheries in networks. Nat. Commun. 7, 10441 (2016)
Virtanen, P., Liukkonen, V., Vahtera, J., Kivimäki, M., Koskenvuo, M.: Health inequalities in the workforce: the labour market core–periphery structure. Int. J. Epidemiol. 32(6), 1015–1021 (2003)
Waenerlund, A.-K., Gustafsson, P.E., Virtanen, P., Hammarström, A.: Is the core-periphery labour market structure related to perceived health? findings of the northern swedish cohort. BMC Public Health 11(1), 956 (2011)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications, vol. 8. Cambridge University Press, Cambridge (1994)
Xiang, B.-B., Bao, Z.-K., Ma, C., Zhang, X., Chen, H.-S., Zhang, H.-F.: A unified method of detecting core-periphery structure and community structure in networks. Chaos Interdiscip. J. Nonlinear Sci. 28(1), 013122 (2018)
Xie, J., Kelley, S., Szymanski, B.K.: Overlapping community detection in networks: the state-of-the-art and comparative study. Acm Comput. Surv. (csur) 45(4), 43 (2013)
Yan, B., Luo, J.: Multicores-periphery structure in networks. Netw. Sci. 7(1), 70–87 (2019)
Yang, J., et al.: Structural correlation between communities and core-periphery structures in social networks: evidence from Twitter data. Expert Syst. Appl. 111, 91–99 (2018)
Yang, J., Leskovec, J.: Overlapping communities explain core–periphery organization of networks. Proc. IEEE 102(12), 1892–1902 (2014)
Yuan, P., Ma, H.: Hug: Human gathering point based routing for opportunistic networks. In: 2012 IEEE Wireless Communications and Networking Conference (WCNC). IEEE (2012)
Zhang, Y., Friend, A.J., Traud, A.L., Porter, M.A., Fowler, J.H., Mucha, P.J.: Community structure in congressional cosponsorship networks. Phys. A Stat. Mech. Appl. 387(7), 1705–1712 (2008)
Zhang, X., Martin, T., Newman, M.E.J.: Identification of core-periphery structure in networks. Phys. Rev. E 91(3), 032803 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tang, W., Zhao, L., Liu, W. et al. Recent advance on detecting core-periphery structure: a survey. CCF Trans. Pervasive Comp. Interact. 1, 175–189 (2019). https://doi.org/10.1007/s42486-019-00016-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42486-019-00016-z