Networks in life: Scaling properties and eigenvalue spectra. (English) Zbl 1001.92025

Summary: We analyze growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and hierarchical organization of these graphs, a deterministic construction is also used. We demonstrate the use of determining the eigenvalue spectra of sparse random graph models for the categorization of small measured networks.


92C37 Cell biology
05C80 Random graphs (graph-theoretic aspects)
Full Text: DOI arXiv


[1] Erdős, P; Rényi, A, On the evolution of random graphs, Publ. math. inst. hung. acad. sci., 5, 17-61, (1960) · Zbl 0103.16301
[2] Watts, D.J, Small world, (1999), Princeton University Press Princeton, NJ
[3] Watts, D.J; Strogatz, S.H, Collective dynamics of small-world networks, Nature, 393, 440-442, (1998) · Zbl 1368.05139
[4] Barabási, A.-L; Ravasz, E; Vicsek, T, Deterministic scale-free networks, Physica A, 299, 559-564, (2001) · Zbl 0972.57003
[5] Dorogovtsev, S.N; Goltsev, A.V; Mendes, J.F.F, Pseudofractal scale-free web, Phys. rev. E, 65, 066122, (2002)
[6] Jung, S; Kim, S; Kahng, B, Phys. rev. E, 65, 056101, (2002)
[7] Wasserman, S; Faust, K, Social network analysis, (1994), Cambridge University Press Cambridge
[8] M. Kochen (Ed.), The Small World, Ablex, Norwood, NJ, 1989.
[9] Amaral, L.A.N; Scala, A; Barthélémy, M; Stanley, H.E, Proc. nat. acad. sci. USA, 97, 11149, (2000)
[10] Albert, R; Barabási, A.L, Phys. rev. lett., 85, 5234, (2000)
[11] Albert, R; Jeong, H; Barabási, A.L, Nature, 400, 130, (1999)
[12] Lawrence, S; Giles, C.L, Nature, 400, 107, (1999)
[13] Huberman, B.A; Adamic, L.A, Nature, 401, 131, (1999)
[14] Jeong, H, Nature, 407, 651, (2000)
[15] R.V. Solé, J.M. Montoya, 2000, cond-mat/0011196.
[16] Newman, M.E.J, Proc. nat. acad. sci. USA, 98, 404, (2001)
[17] Newman, M.E.J, Phys. rev. E, 64, 016131, (2001)
[18] Dorogovtsev, S.N; Mendes, J.F.F, Europhys. lett., 52, 33, (2000)
[19] Dorogovtsev, S.N; Mendes, J.F.F, Phys. rev. E, 62, 1842, (2000)
[20] Krapivsky, P.L; Redner, S; Leyvraz, F, Phys. rev. lett., 85, 4629, (2000)
[21] J.M. Montoya, R.V. Solé, Small World Patterns in Food Webs, cond-mat/0011195.
[22] Wuchty, S, Scale-free behavior in protein domain networks, Mol. biol. evol., 18, 1694-1702, (2001)
[23] I.J. Farkas, H. Jeong, T. Vicsek, A.-L. Barabási, Z.N. Oltvai, The topology of the transcription regulatory network in the yeast, S. cerevisiae, to be published.
[24] I.J. Farkas, I. Derényi, A.-L. Barabási, T. Vicsek, Phys. Rev. E 64 (2001) 026704:1-12.
[25] Bauer, M; Golinelli, O, Random incidence matricesmoments of the spectral density, J. statist. phys., 103, 301-337, (2001) · Zbl 0999.82035
[26] Goh, K.-I; Kahng, B; Kim, D, Spectra and eigenvectors of scale-free networks, Phys. rev. E, 64, 051903, (2001)
[27] Cvetković, D.M; Doob, M; Sachs, H, Spectra of graphs—theory and applications, (1995), Johann Ambrosius Barth Verlag Heidelberg-Leipzig
[28] Mehta, M.L, Random matrices, (1991), Academic Press New York
[29] Hughes, T.R, Functional discovery via a compendium of expression profiles, Cell, 102, 109-126, (2000)
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