Abstract
Social networks are discrete systems with a large amount of heterogeneity among nodes (individuals). Measures of centrality aim at a quantification of nodes’ importance for structure and function. Here we ask to which extent the most central nodes can be found by purely local search. We find that many networks have close-to-optimal searchability under eigenvector centrality, outperforming searches for degree and betweenness. Searchability of the strongest spreaders in epidemic dynamics tends to be substantially larger for supercritical than for subcritical spreading.
Similar content being viewed by others
References
Adamic, L.A., Lukose, R.M., Puniyani, A.R., Huberman, B.A.: Search in power-law networks. Phys. Rev. E 64, 046135 (2001)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Alon, U.: An Introduction to Systems Biology: Design Principles of Biological Circuits. CRC Press, Taylor & Francis, Boca Raton (2006)
Axelsen, J.B., Bernhardsson, S., Rosvall, M., Sneppen, K., Trusina, A.: Degree landscapes in scale-free networks. Phys. Rev. E 74, 036119 (2006)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Barabási, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272, 173–187 (1999)
Bascompte, J.: Networks in ecology. Basic Appl. Ecol. 8, 485–490 (2007)
Boguñá, M., Pastor-Satorras, R., Díaz-Guilera, A., Arenas, A.: Models of social networks based on social distance attachment. Phys. Rev. E 70, 056122 (2004)
Boguñá, M., Krioukov, D., Claffy, K.C.: Navigability of complex networks. Nat. Phys. 5, 74–80 (2009)
Chakrabarti, D., Wang, Y., Wang, C., Leskovec, J., Faloutsos, C.: Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 10(4), 1:1–1:26 (2008)
Cohen, R., Havlin, S., ben Avraham, D: Efficient immunization strategies for computer networks and populations. Phys. Rev. Lett. 91, 247901 (2003)
Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill, New York (2001)
Diestel, R.: Graph Theory. Springer, Heidelberg (2010)
Dodds, P.S., Muhamad, R., Watts, D.J.: An experimental study of search in global social networks. Science 301(5634), 827–829 (2003)
Dorogovtsev, S.: Lectures on Complex Networks. Oxford Master Series in Statistical, Computational, and Theoretical Physics. Oxford University Press, London (2010)
Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of growing networks with preferential linking. Phys. Rev. Lett. 85, 4633–4636 (2000)
Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Size-dependent degree distribution of a scale-free growing network. Phys. Rev. E 63, 062101 (2001)
Eguíluz, V.M., Klemm, K.: Epidemic threshold in structured scale-free networks. Phys. Rev. Lett. 89, 108701 (2002)
Erdős, P., Renyi, A.: On random graphs. Publ. Math. (Debr.) 6, 290–297 (1959)
Gilbert, E.N.: Random graphs. Ann. Math. Stat. 4, 1141–1144 (1959)
Gleiser, P.M., Danon, L.: Community structure in jazz. Adv. Complex Syst. 6(4), 565–573 (2003)
Grabowicz, P.A., Eguíluz, V.M.: Heterogeneity shapes groups growth in social online communities. Europhys. Lett. 97(2), 28002 (2012)
Grimmett, G.: Percolation. Grundlehren der mathematischen Wissenschaften. Springer, Berlin (1999). books.google.ch/books?id=lTSzVXTOCpIC
Guimerá, R., Danon, L., Díaz-Guilera, A., Giralt, F., Arenas, A.: Self-similar community structure in a network of human interactions. Phys. Rev. E 68, 065103 (2003)
Keeling, M.J., Eames, K.T.: Networks and epidemic models. J. R. Soc. Interface 2(4), 295–307 (2005)
Kitsak, M., Gallos, L.K., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identifying influential spreaders in complex networks. Nat. Phys. 6, 888–893 (2010)
Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)
Klemm, K., Eguíluz, V.M.: Growing scale-free networks with small-world behavior. Phys. Rev. E 65, 057102 (2002)
Klemm, K., Eguíluz, V.M.: Highly clustered scale-free networks. Phys. Rev. E 65, 036123 (2002)
Klemm, K., Serrano, M.A., Eguiluz, V.M., San Miguel, M.: A measure of individual role in collective dynamics. Sci. Rep. 2, 292 (2012)
Koschützki, D., Lehmann, K., Peeters, L., Richter, S., Tenfelde-Podehl, D., Zlotowski, O.: Centrality indices. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. Lecture Notes in Computer Science, vol. 3418, pp. 16–61. Springer, Berlin/Heidelberg (2005)
Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of growing random networks. Phys. Rev. Lett. 85, 4629–4632 (2000). link.aps.org/doi/10.1103/PhysRevLett.85.4629.
Milgram, S.: The small-world problem. Psychol. Today 1(1), 61–67 (1967)
Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6(2–3), 161–180 (1995)
Moore, C., Mertens, S.: The Nature of Computation. Oxford University Press, London (2011)
Newman, M.: Networks: An Introduction. Oxford University Press, New York (2010)
Newman, M.E.J.: The structure of scientific collaboration networks. Proc. Natl. Acad. Sci. USA 98(2), 404–409 (2001)
Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66, 016128 (2002)
Nitschke, J.R.: Systems chemistry: molecular networks come of age. Nature 462, 736–738 (2009)
Onnela, J.P., Saramäki, J., Hyvönen, J., Szabó, G., Lazer, D., Kaski, K., Kertész, J., Barabási, A.L.: Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. 104(18), 7332–7336 (2007)
Pastor-Satorras, R., Vespignani, A.: Immunization of complex networks. Phys. Rev. E 65, 036104 (2002)
Price, D.d.S.: A general theory of bibliometric and other cumulative advantage processes. J. Am. Soc. Inf. Sci. 27(5), 292–306 (1976)
Rao, A.R., Jana, R., Bandyopadhyay, S.: A Markov chain Monte Carlo method for generating random (0,1)-matrices with given marginals. Indian J. Stat. 58(2), 225–242 (1996)
Rosvall, M., Grönlund, A., Minnhagen, P., Sneppen, K.: Searchability of networks. Phys. Rev. E 72, 046117 (2005)
Sneppen, K., Trusina, A., Rosvall, M.: Hide-and-seek on complex networks. Europhys. Lett. 69(5), 853–859 (2005)
Thulasiraman, K., Swamy, M.N.S.: Graphs: Theory and Algorithms. Wiley, New York (1991)
Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)
Wuchty, S., Stadler, P.F.: Centers of complex networks. J. Theor. Biol. 223, 45–53 (2003)
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33(4), 452–473 (1977)
Author information
Authors and Affiliations
Corresponding author
Additional information
The author acknowledges funding from Volkswagenstiftung.
Rights and permissions
About this article
Cite this article
Klemm, K. Searchability of Central Nodes in Networks. J Stat Phys 151, 707–719 (2013). https://doi.org/10.1007/s10955-013-0727-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-013-0727-7