Abstract
We propose a two-component growing network model which comprises two kinds of nodes. Such a network is constructed by introducing new nodes of either kind with no immediate links and creating new links between any two nodes. We then investigate the connectivity of the two-component growing network by means of the rate equation approach. For a network system with shifted linear connection rate kernels, the in-degree and out-degree distributions take power-law forms; while for a random growing network, the in-degree and out-degree distributions are both exponential. Moreover, the in-degree and out-degree distributions are correlated each other.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bollobási, B.: Random Graphs. Academic Press, London (1985)
Albert, R., Jeong, H., Barabási, A.L.: Diameter of the world-wide web. Nature 401, 130–131 (1999)
Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87, 258701 (2001)
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.-L.: The large-scale organization of metabolic networks. Nature 407, 651–654 (2000)
Newman, M.E.J.: Scientific collaboration networks. I. network construction and fundamental results. Phys. Rev. E 64, 016131 (2001)
Newman, M.E.J.: Scientific collaboration networks. II. shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016132 (2001)
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)
Liljeros, F., Edling, C.R., Amaral, L.A.N., Stanley, H.E., Åberg, Y.: The web of human sexual contacts. Nature 411, 907–908 (2001)
Watts, D.J., Strogatz, S.H.: Collective dynamics of “small-world network”. Nature 393, 440–442 (1998)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Newman, M.E.J., Moore, C., Watts, D.J.: Mean-field solution of the small-world network model. Phys. Rev. Lett. 84, 3201–3204 (2000)
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.: Evolution of networks with aging of sites. Phys. Rev. E 62, 1842–1845 (2000)
Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of growing random networks. Phys. Rev. Lett. 85, 4629–4632 (2000)
Krapivsky, P.L., Rodgers, G.J., Redner, S.: Degree distributions of growing networks. Phys. Rev. Lett. 86, 5401–5404 (2001)
Krapivsky, P.L., Redner, S.: Organization of growing random networks. Phys. Rev. E 63, 066123 (2001)
Cheng, X., Wang, H., Ouyang, Q.: Scale-free network model of node and connection diversity. Phys. Rev. E 65, 066115 (2002)
Kim, J.-W., Hunt, B., Ott, E.: Evolving networks with multispecies nodes and spread in the number of initial links. Phys. Rev. E 66, 046115 (2002)
Kohn, K.W.: Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol. Biol. Cell 10, 2703–2734 (1999)
Ke, J.: Scale-free multicomponent growing networks. Phys. Rev. E 69, 037101 (2004)
Krapivsky, P.L., Redner, S.: Finiteness and fluctuations in growing networks. J. Phys. A: Math. Gen. 35, 9517–9534 (2002)
Dorogovtsev, S.N., Mendes, J.F.F.: Scaling properties of scale-free evolving networks: continuous approach. Phys. Rev. E 63, 056125 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Ke, J., Chen, X. (2009). Degree Distribution of a Two-Component Growing Network. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_60
Download citation
DOI: https://doi.org/10.1007/978-3-642-02469-6_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02468-9
Online ISBN: 978-3-642-02469-6
eBook Packages: Computer ScienceComputer Science (R0)