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Volumn 67, Issue 2 2, 2003, Pages 261261-2612613

Mixing patterns in networks

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DATA STRUCTURES; GRAPH THEORY; MONTE CARLO METHODS; NUMERICAL METHODS;

EID: 0038752085     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (2403)

References (80)
  • 23
    • 33645080272 scopus 로고    scopus 로고
    • note
    • ij is defined as the probability that a randomly chosen edge is connected to a vertex of type i at its A end and type j at its B end. Thus every edge, whether it joins unlike vertices or like ones, appears only once in the matrix - no edge appears both above and below the diagonal. It is possible to construct a theory in which the ends of undirected edges are indistinguishable, but in this case each edge that joins unlike vertices appears twice in the matrix, both above and below the diagonal, and edges joining like vertices appear only once. This necessitates the introduction of an extra factor of 2 into the off-diagonal terms. This approach is adopted for example in Ref. [43].
  • 31
    • 0001622847 scopus 로고
    • Poznań, edited by A. M. Frieze and T. Łuczak (Wiley, New York
    • T. Łuczak, in Proceedings of the Symposium on Random Graphs, Poznań 1989, edited by A. M. Frieze and T. Łuczak (Wiley, New York, 1992), pp. 165-182.
    • (1989) Proceedings of the Symposium on Random Graphs , pp. 165-182
    • Łuczak, T.1
  • 38
    • 0004705831 scopus 로고    scopus 로고
    • U.S. Department of Health and Human Services, National Center for Health Statistics, Hyattsville, MD
    • National Survey of Family Growth, Cycle V, 1995 (U.S. Department of Health and Human Services, National Center for Health Statistics, Hyattsville, MD, 1997).
    • (1997) National Survey of Family Growth, Cycle V, 1995
  • 39
    • 33645094754 scopus 로고    scopus 로고
    • note
    • Perhaps it is stretching a point a little to regard links between marriage partners as forming a network, since presumably most people have only one marriage at a time. However, if we view the ages of marriage partners as a guide to the ages of sexual partners in general, then the resulting assortative mixing also describes networks of such more general partnerships, which are certainly very real [25,26,49,64].
  • 41
    • 33645078722 scopus 로고    scopus 로고
    • e-print cond-mat/0205379
    • S. Maslov and K. Sneppen, e-print cond-mat/0205379.
    • Maslov, S.1    Sneppen, K.2
  • 43
    • 33645059785 scopus 로고    scopus 로고
    • e-print cond-mat/0207035.
    • A. Vazquez and M. Weigt, e-print cond-mat/0207035.
    • Vazquez, A.1    Weigt, M.2
  • 45
    • 33645084339 scopus 로고    scopus 로고
    • note
    • One can also calculate a value for r by simply ignoring the directed nature of the edges in a directed network. This approach, which we adopted in Ref. [22], will in general give a different figure from that given by Eq. (25). While Eq. (25) will normally give a more meaningful result for a directed network, there may be cases in which ignoring direction is the correct thing to do. For example, in a food web one might only be interested in which species have tropic relations with with others, and not in which direction that relation lies in terms of energy or carbon flow.
  • 60
    • 33645048809 scopus 로고    scopus 로고
    • note
    • -1 and is small compared with other sources of error in our simulations.
  • 66
    • 33645073493 scopus 로고    scopus 로고
    • note
    • Not all graphs with r = 0 are without degree correlations. A measurement of r = 0 implies only that the mean degree correlation is zero when averaged over all degrees. The grown graph model of Barabási and Albert [6] provides an example of a network that possesses degree correlations although it has r = 0 [22].
  • 68
    • 33645065692 scopus 로고    scopus 로고
    • note
    • The degree is not recalculated after each removal. Removal is in the order of vertices' starting degree in the network before any deletion has taken place.
  • 80
    • 33645057018 scopus 로고    scopus 로고
    • e-print cond-mat/0210362
    • A. Vazquez and Y. Moreno, e-print cond-mat/0210362.
    • Vazquez, A.1    Moreno, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.