A Monte Carlo model for networks between professionals and society

We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, P(k)∼k-γ, with γ ranging from 0.2 to 0.5, small-world properties, with a network diameter following D(N)∼logN and relative high clustering, following C(N)∼1/N and C(k)∼k-α, with α close to 3. We compare our results with data from real-world protein interaction networks.

[1]  Y. Moreno,et al.  Resilience to damage of graphs with degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[3]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[4]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[5]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[6]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[7]  S. S. Manna,et al.  Scale-free networks from a Hamiltonian dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  K. Goh,et al.  Betweenness centrality correlation in social networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[10]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  A. Barabasi,et al.  Functional and topological characterization of protein interaction networks , 2004, Proteomics.

[12]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[13]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[14]  J. Hołyst,et al.  Statistical analysis of 22 public transport networks in Poland. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  F. Vesely,et al.  Computational Physics: An Introduction , 1996 .

[16]  Jian Wang,et al.  Protein interaction networks of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster: Large‐scale organization and robustness , 2006, Proteomics.

[17]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[18]  S. Redner How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[19]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[20]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Tom Lenaerts,et al.  Growing biological networks: beyond the gene-duplication model. , 2006, Journal of theoretical biology.

[22]  S. L. Wong,et al.  A Map of the Interactome Network of the Metazoan C. elegans , 2004, Science.

[23]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  I. Sokolov,et al.  Correlations in scale-free networks: tomography and percolation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[26]  D. Kofke,et al.  Variational formula for the free energy based on incomplete sampling in a molecular simulation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[29]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[30]  C. Caroli,et al.  A phenomenology of boundary lubrication: the lumped junction model , 1998 .

[31]  Robin E. C. Lee,et al.  The yeast kinome displays scale free topology with functional hub clusters , 2005, BMC Bioinformatics.