The von Neumann entropy of networks

  title={The von Neumann entropy of networks},
  author={Filippo Passerini and Simone Severini},
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graph-theoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the number of connected components, long paths and nontrivial symmetries. When the set of vertices is… CONTINUE READING
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