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We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian's Von Neumann entropy as a measure of bipartite entanglement present between...
We analyze topological entropy in wireless networks that are subject to local scattering and macroscopic shadowing effects. To this end, we model a network as a random geometric graph with probabilistic pair connections (due to channel randomness) and define uncertainty as the Shannon entropy of the underlying graph ensemble. We present new bounds on topological entropy that are functionals of the...
We study the effect of anisotropic radiation on wireless network complexity. To this end, we model a wireless network as a random geometric graph where nodes have random antenna orientations as well as random positions, and communication is affected by Rayleigh fading. Complexity is quantified by computing the Shannon entropy of the underlying graph model. We use this formalism to develop analytic...
This work provides an analysis of topological uncertainty in wireless networks. Here, we model a wireless network as a random geometric graph (RGG) and quantify topological uncertainty in terms of the Shannon entropy of the underlying graph model. Direct pairwise connections between nodes are probabilistic in general, and thus our analysis covers cases where channel randomness contributes to uncertainty...
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