The Laplacian spectrum of a graph
SIAM Journal on Matrix Analysis and Applications
Elements of information theory
Elements of information theory
Quantum computation and quantum information
Quantum computation and quantum information
Combinatorial laplacians and positivity under partial transpose
Mathematical Structures in Computer Science
A history of graph entropy measures
Information Sciences: an International Journal
Graph complexity from the jensen-shannon divergence
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Graph Kernels from the Jensen-Shannon Divergence
Journal of Mathematical Imaging and Vision
Depth-based complexity traces of graphs
Pattern Recognition
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The authors introduce a novel entropic notion with the purpose of quantifying disorder/uncertainty in networks. This is based on the Laplacian and it is exactly the von Neumann entropy of certain quantum mechanical states. 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 number of its connected components. The notion opens the perspective of a wide interface between quantum information theory and the study of complex networks at the statistical level.