Spectral Properties of the Threshold Network Model

We study the spectral distribution of the threshold network model. The results contain an explicit description of the distribution and its asymptotic behavior.

[1]  Svante Janson,et al.  Threshold Graph Limits and Random Threshold Graphs , 2008, Internet Math..

[2]  R. Pastor-Satorras,et al.  Class of correlated random networks with hidden variables. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  On asymptotic properties of the rank of a special random adjacency matrix , 2007 .

[4]  N. Konno,et al.  Limit Theorems for the Average Distance and the Degree Distribution of the Threshold Network Model , 2009 .

[5]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[6]  M. Uchida,et al.  Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory , 2009, 0911.3864.

[7]  R. Roy,et al.  Rigorous results on the threshold network model , 2005, math/0505681.

[8]  Naoki Masuda,et al.  VIP-club phenomenon: Emergence of elites and masterminds in social networks , 2006, Soc. Networks.

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

[10]  B. Söderberg General formalism for inhomogeneous random graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[12]  N. Konno,et al.  Limit theorems for some statistics of a generalized threshold network model(Theory of Biomathematics and its Applications III) , 2007 .

[13]  R. Merris Laplacian graph eigenvectors , 1998 .

[14]  A. Hagberg,et al.  Designing threshold networks with given structural and dynamical properties. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  U Cnrs Complex Networks: Structure and Dynamics , 2006 .

[16]  N. Konno,et al.  Statistical Properties of a Generalized Threshold Network Model , 2007, 0707.1744.

[17]  Hiroyoshi Miwa,et al.  Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Caldarelli,et al.  Vertex intrinsic fitness: how to produce arbitrary scale-free networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  N. Mahadev,et al.  Threshold graphs and related topics , 1995 .

[20]  N. Konno,et al.  Geographical threshold graphs with small-world and scale-free properties. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Spectral properties of disordered fully connected graphs. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  R. Merris Degree maximal graphs are Laplacian integral , 1994 .

[23]  A. Hora,et al.  Quantum Probability and Spectral Analysis of Graphs , 2007 .