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Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia

A. Capocci, V. D. P. Servedio, F. Colaiori, L. S. Buriol, D. Donato, S. Leonardi, and G. Caldarelli
Phys. Rev. E 74, 036116 – Published 25 September 2006
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    Abstract

    We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.

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    • Received 17 February 2006

    DOI:https://doi.org/10.1103/PhysRevE.74.036116

    ©2006 American Physical Society

    Authors & Affiliations

    A. Capocci1, V. D. P. Servedio1,2, F. Colaiori3, L. S. Buriol2,4, D. Donato2, S. Leonardi2, and G. Caldarelli1,3

    • 1Centro Studi e Ricerche E. Fermi, Compendio Viminale, Roma, Italy
    • 2Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza,” Via Salaria 113, 00198 Roma, Italy
    • 3CNR-INFM(SMC) Istituto dei Sistemi Complessi and Dipartimento di Fisica, Università di Roma “La Sapienza,” Piazzale Aldo Moro 2, 00185, Roma, Italy
    • 4Computer Science Department, Federal University of Rio Grande do Sul, Porto Alegre/RS, Brazil

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    Issue

    Vol. 74, Iss. 3 — September 2006

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    Images

    • Figure 1
      Figure 1
      The shape of the Wikipedia network.Reuse & Permissions
    • Figure 2
      Figure 2
      In-degree (white symbols) and out-degree (filled symbols) distributions for the Wikipedia English (circles) and Portuguese (triangles) graph. The solid line and the dashed line represent simulation results for the in-degree and the out-degree respectively, for a number of 10 edges added to the network per time step. Dotted-dashed lines show the kin,out−2.1 (bottom line) and the kin,out−2 (top line) behavior, as a guide for the eye.Reuse & Permissions
    • Figure 3
      Figure 3
      The preferential attachment for the in degree and the out degree in the English and Portuguese Wikipedia network. The solid line represents the linear preferential attachment hypothesis Π∼kin,out.Reuse & Permissions
    • Figure 4
      Figure 4
      The average observed neighbors’ in degree, computed along incoming edges, as a function of the in degree in the case of the English (circles) and Portuguese (triangles) Wikipedia, compared to the simulations of the model with N=20000, M=10, R1=0.026 and R2=0.091 (dashed line above), averaged over 100 realizations. A version of the same model where the first 0.5% of vertices have been removed to reduce the initial condition impact, is also shown as the thick solid line through the observed data.Reuse & Permissions
    • Figure 5
      Figure 5
      (Color online) First 100 eigenvalues of the normal matrix associated to the measured Portuguese Wikipedia (circles), to the network of the same order generated by our model (triangles), and the binomial network of the same order and average degree (diamonds). The presence of a clear community structure is revealed by the large number of eigenvalues around the unity.Reuse & Permissions
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