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Differential equation approximations of stochastic network processes: An operator semigroup approach
A sufficient condition for classified networks to possess complex network features
1.  College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China, China, China 
2.  College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210046, China 
References:
[1] 
R. Albert and A.L. Barabási, Emergence of scaling in random networks, Science, 286 (1999), 509512. doi: 10.1126/science.286.5439.509. 
[2] 
R. Albert and A.L. Barabási, Statistical mechanics of complex networks, Reviews of Mordern Physics, 74 (2002), 4797. doi: 10.1103/RevModPhys.74.47. 
[3] 
D. J. Aldous, A tractable complex network model based on the stochastic meanfield model of distance, in "Complex Networks," Lecture Notes in Physics, 650, Springer, Berlin, (2004), 5187. 
[4] 
D. J. Aldous and W. S. Kendall, Shortlength routes in lowcost networks via Poisson line patterns, Advances in Applied Probability, 40 (2008), 121. doi: 10.1239/aap/1208358883. 
[5] 
H. G. Bartel, H. J. Mucha and J. Dolata, On a modified graphtheoretic partitioning method of cluster analysis, MatchCommunications in Mathematical and in Computer Chemistry, 48 (2003), 209233. 
[6] 
B. Bollobás, S. Janson and O. Riordan, The phase transition in inhomogeneous random graphs, Random Structures and Algorithms, 31 (2007), 3122. doi: 10.1002/rsa.20168. 
[7] 
A. DiazGuilera, Complex networks: Statics and dynamics, Advanced Summer School in Physics 2006, 885 (2007), 107128. 
[8] 
Z. P. Fan, G. R. Chen and Y. N. Zhang, A comprehensive multilocalworld model for complex networks, Physics Letters A, 373 (2009), 16011605. doi: 10.1016/j.physleta.2009.02.072. 
[9] 
A. Ganesh and F. Xue, On the connectivity and diameter of smallworld networks, Advances in Applied Probability, 39 (2007), 853863. doi: 10.1239/aap/1198177228. 
[10] 
P. Holme and B. J. Kim, Growing scalefree networks with tunable clustering, Physical Review E, 65 (2002), 026107. 
[11] 
G. Lee and G. I. Kim, Degree and wealth distribution in a network, Physica AStatistical Mechanics and its Applications, 383 (2007), 677686. 
[12] 
N. Miyoshi, T. Shigezumi, R. Uehara and O. Watanabe, Scale free interval graphs, Theoretical Computer Science, 410 (2009), 45884600. doi: 10.1016/j.tcs.2009.08.012. 
[13] 
Y. Ou and C.Q. Zhang, A new multimembership clustering method, Journal of Industrial and Management Optimization, 3 (2007), 619624. doi: 10.3934/jimo.2007.3.619. 
[14] 
M. M. Sørensen, btree facets for the simple graph partitioning polytope, Journal of Combinatorial Optimization, 8 (2004), 151170. doi: 10.1023/B:JOCO.0000031417.96218.26. 
[15] 
J. Szymański, Concentration of vertex degrees in a scalefree random graph process, Random Structures and Algorithms, 26 (2005), 224236. doi: 10.1002/rsa.20065. 
[16] 
D. J. Watts and S. H. Strogatz, Collective dynamics of 'smallworld' networks, Nature, 393 (1998), 440442. doi: 10.1038/30918. 
show all references
References:
[1] 
R. Albert and A.L. Barabási, Emergence of scaling in random networks, Science, 286 (1999), 509512. doi: 10.1126/science.286.5439.509. 
[2] 
R. Albert and A.L. Barabási, Statistical mechanics of complex networks, Reviews of Mordern Physics, 74 (2002), 4797. doi: 10.1103/RevModPhys.74.47. 
[3] 
D. J. Aldous, A tractable complex network model based on the stochastic meanfield model of distance, in "Complex Networks," Lecture Notes in Physics, 650, Springer, Berlin, (2004), 5187. 
[4] 
D. J. Aldous and W. S. Kendall, Shortlength routes in lowcost networks via Poisson line patterns, Advances in Applied Probability, 40 (2008), 121. doi: 10.1239/aap/1208358883. 
[5] 
H. G. Bartel, H. J. Mucha and J. Dolata, On a modified graphtheoretic partitioning method of cluster analysis, MatchCommunications in Mathematical and in Computer Chemistry, 48 (2003), 209233. 
[6] 
B. Bollobás, S. Janson and O. Riordan, The phase transition in inhomogeneous random graphs, Random Structures and Algorithms, 31 (2007), 3122. doi: 10.1002/rsa.20168. 
[7] 
A. DiazGuilera, Complex networks: Statics and dynamics, Advanced Summer School in Physics 2006, 885 (2007), 107128. 
[8] 
Z. P. Fan, G. R. Chen and Y. N. Zhang, A comprehensive multilocalworld model for complex networks, Physics Letters A, 373 (2009), 16011605. doi: 10.1016/j.physleta.2009.02.072. 
[9] 
A. Ganesh and F. Xue, On the connectivity and diameter of smallworld networks, Advances in Applied Probability, 39 (2007), 853863. doi: 10.1239/aap/1198177228. 
[10] 
P. Holme and B. J. Kim, Growing scalefree networks with tunable clustering, Physical Review E, 65 (2002), 026107. 
[11] 
G. Lee and G. I. Kim, Degree and wealth distribution in a network, Physica AStatistical Mechanics and its Applications, 383 (2007), 677686. 
[12] 
N. Miyoshi, T. Shigezumi, R. Uehara and O. Watanabe, Scale free interval graphs, Theoretical Computer Science, 410 (2009), 45884600. doi: 10.1016/j.tcs.2009.08.012. 
[13] 
Y. Ou and C.Q. Zhang, A new multimembership clustering method, Journal of Industrial and Management Optimization, 3 (2007), 619624. doi: 10.3934/jimo.2007.3.619. 
[14] 
M. M. Sørensen, btree facets for the simple graph partitioning polytope, Journal of Combinatorial Optimization, 8 (2004), 151170. doi: 10.1023/B:JOCO.0000031417.96218.26. 
[15] 
J. Szymański, Concentration of vertex degrees in a scalefree random graph process, Random Structures and Algorithms, 26 (2005), 224236. doi: 10.1002/rsa.20065. 
[16] 
D. J. Watts and S. H. Strogatz, Collective dynamics of 'smallworld' networks, Nature, 393 (1998), 440442. doi: 10.1038/30918. 
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