21,035 research outputs found
Testing goodness-of-fit of random graph models
Random graphs are matrices with independent 0, 1 elements with probabilities
determined by a small number of parameters. One of the oldest model is the
Rasch model where the odds are ratios of positive numbers scaling the rows and
columns. Later Persi Diaconis with his coworkers rediscovered the model for
symmetric matrices and called the model beta. Here we give goodnes-of-fit tests
for the model and extend the model to a version of the block model introduced
by Holland, Laskey, and Leinhard
Synchronization in random networks with given expected degree sequences
Synchronization in random networks with given expected degree sequences is studied. We also investigate in details the synchronization in networks whose topology is described by classical random graphs, power-law random graphs and hybrid graphs when N goes to infinity. In particular, we show that random graphs almost surely synchronize. We also show that adding small number of global edges to a local graph makes the corresponding hybrid graph to synchroniz
Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees
In this paper, we analyze the limiting spectral distribution of the adjacency
matrix of a random graph ensemble, proposed by Chung and Lu, in which a given
expected degree sequence
is prescribed on the ensemble. Let if there is an edge
between the nodes and zero otherwise, and consider the normalized
random adjacency matrix of the graph ensemble: . The empirical spectral distribution
of denoted by is the empirical
measure putting a mass at each of the real eigenvalues of the
symmetric matrix . Under some technical conditions on the
expected degree sequence, we show that with probability one,
converges weakly to a deterministic
distribution . Furthermore, we fully characterize this
distribution by providing explicit expressions for the moments of
. We apply our results to well-known degree distributions,
such as power-law and exponential. The asymptotic expressions of the spectral
moments in each case provide significant insights about the bulk behavior of
the eigenvalue spectrum
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