Characteristics of certain families of random graphs
Date
2009
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Abstract
Many random network models can be expressed as the product space of the probability space of the individual edges. In these cases, the model can be expressed using a matrix of the probabilities of each edge. I then analyze these models using their respective probability matrices. Degree distribution and the larger eigenvalues are among the attributes whose values can be bound by examining the same attributes of the probability matrix. I also bound the difference between the eigenvalues of the adjacency matrix of a member of a random graph model and the eigenvalues of the probability matrix for the model. In addition I find the neighborhood expansion properties for three separate edge-product models.
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Subject
edge products
probability matrices
random graphs
mathematics