On the von neumann entropy of graphs
Web19 de fev. de 2024 · The von Neumann graph entropy is a measure of graph complexity based on the Laplacian spectrum. It has recently found applications in various learning … WebThe von Neumann entropy is also strongly subadditive.Given three Hilbert spaces, A, B, C, + () + ().This is a more difficult theorem and was proved first by J. Kiefer in 1959 and independently by Elliott H. Lieb and Mary Beth Ruskai in 1973, using a matrix inequality of Elliott H. Lieb proved in 1973. By using the proof technique that establishes the left side …
On the von neumann entropy of graphs
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Web30 de dez. de 2010 · We prove that the von Neumann entropy of the typical Erdös–Rényi random graph saturates its upper bound. Since connected regular graphs saturate this … Web11 de dez. de 2024 · The von Neumann entropy was originally introduced by von Neumann around 1927 for proving the irreversibility of quantum measurement …
http://proceedings.mlr.press/v97/chen19j/chen19j.pdf Webwhere S(σAB) is the von Neumann entropy of the separable density matrix and KAB is the modular Hamiltonian of ρ0 AB, K0 AB = −logρ0 AB. (20) 3.2 The calculation of S(σAB) In …
Web1 de out. de 2009 · It is remarkable that the von Neumann entropy depends on spectral properties and it can be computed efficiently. The analytical results described here and the numerical computations lead us to conclude that the von Neumann entropy increases under edge addition, increases with the regularity properties of the network and with the … Web1 de dez. de 2010 · We consider the von Neumann entropy (Du et al. 2010; Feng et al. 2024), also known as Laplacian graph entropy, which recently found notable applications in complex networks analysis and pattern ...
WebOn the von neumann entropy of graphs. Journal of Complex Networks, 7(4):491–514, 2024. Francesco Ortelli and Sara Van De Geer. Adaptive rates for total variation image …
WebThe denition of von Neumann entropy is equivalent to H = P n i=1 i ln i, where the convention 0ln0 = 0 is used due to lim x ! 0 + x ln x = 0 . Moreover, since P i i = 1 and i 0 for all i, the von Neumann entropy can be viewed as the Shannon entropy associated with the eigenspectrum f ign i=1. We consider the class of undirected weighted simple non- how does a fire truck soundWeb1 de nov. de 2012 · We pose the von Neumann entropy as a new graph complexity measure. We show how this entropy can be efficiently computed using node degree statistics. We reveal the link between the Estrada’s heterogeneity index and the commute time. We embed von Neumann entropy into the thermodynamic depth to characterize … phop phra hospitalWeb12 de mai. de 2014 · Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein … how does a fire spreadWebFor example, the von Neumann graph entropy facilitates the measure of graph similarity via Jensen-Shannon divergence, which could be used to compress multilayer networks [13] and detect anomalies in graph streams [9]. As another example, the von Neumann graph entropy could be used to design edge arXiv:2102.09766v2 [cs.SI] 6 Jan 2024 phop proteinWeb1 de out. de 2024 · A new definition of entropy for hypergraphs is introduced that takes into account the fine structure of a hypergraph by considering its partialhypergraphs, leading … how does a fire spread throughout a buildingWeb12 de nov. de 2024 · The von Neumann graph entropy (VNGE) can be used as a measure of graph complexity, which can be the measure of information divergence and distance between graphs. Since computing VNGE is required to find all eigenvalues, it is computationally demanding for a large-scale graph. We propose novel quadratic … how does a fire pumper truck workWeb24 de jan. de 2024 · Because of the relationship between relative entropy and the Theil index , this motivates us to refer to the bound as the graph’s von Neumann Theil index (Definition 2 below). A corollary to our main result (Corollary 3) also determines a relationship between graph von Neumann entropy and the graph entropy considered … how does a fire truck pump work