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Distance-Dependent Kronecker Graphs for Modeling Social Networks

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3 Author(s)
Bodine-Baron, E. ; Electr. Eng. Dept., California Inst. of Technol., Pasadena, CA, USA ; Hassibi, B. ; Wierman, A.

This paper focuses on a generalization of stochastic Kronecker graphs, introducing a Kronecker-like operator and defining a family of generator matrices H dependent on distances between nodes in a specified graph embedding. We prove that any lattice-based network model with sufficiently small distance-dependent connection probability will have a Poisson degree distribution and provide a general framework to prove searchability for such a network. Using this framework, we focus on a specific example of an expanding hypercube and discuss the similarities and differences of such a model with recently proposed network models based on a hidden metric space. We also prove that a greedy forwarding algorithm can find very short paths of length O((log log n)2) on the hypercube with n nodes, demonstrating that distance-dependent Kronecker graphs can generate searchable network models.

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Selected Topics in Signal Processing, IEEE Journal of  (Volume:4 ,  Issue: 4 )