SpectralEntropyLib

SpectralEntropyLib is an R library providing functions to compute spectral entropies and related information-theoretic quantities for complex networks.
It implements the theoretical framework introduced in:

M. De Domenico, J. Biamonte
Spectral entropies as information-theoretic tools for complex network comparison
Physical Review X, 6(4), 041062 (2016).
https://doi.org/10.1103/PhysRevX.6.041062

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Introduction

Any physical system can be viewed as information implicitly represented in its state.
This library provides computational tools to quantify that information when the system is represented as a network, using techniques inspired by quantum statistical mechanics.

Main tools include:

• Spectral entropies (von Neumann entropy, Rényi q-entropy)
• Generalized divergences (Kullback–Leibler, Jensen–Shannon)
• Information-theoretic distance measures between networks
• Spectral gap profiles and thermodynamic quantities derived from spectra
• Support for edge-colored and multilayer networks
• Visualization utilities for entropy profiles and density matrices

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Installation

Clone this repository and install locally with devtools:

devtools::install("path/to/SpectralEntropyLib")

Dependencies include:

• igraph
• Matrix
• expm
• RSpectra
• ggplot2
• RColorBrewer

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Example

library(SpectralEntropyLib)
library(igraph)

# Example: simple ring graph with 10 nodes
g <- igraph::make_ring(10)

# von Neumann entropy at resolution beta = 0.5
S_vn <- getVNEntropy(g, beta = 0.5)

# Rényi entropy with q = 2
S_renyi <- getRenyiEntropy(g, beta = 0.5, q = 2)

# Jensen–Shannon distance between two networks
g1 <- igraph::make_ring(8)
g2 <- igraph::make_full_graph(8)
dist <- getNetworkDistance(g1, g2, beta = 0.5)

print(S_vn)
print(S_renyi)
print(dist)

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References

If you use SpectralEntropyLib in your work, please cite:

• M. De Domenico, J. Biamonte, Spectral entropies as information-theoretic tools for complex network comparison, Physical Review X 6, 041062 (2016).
  https://doi.org/10.1103/PhysRevX.6.041062

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Citation

@article{dedomenico2016spectral,
  title={Spectral entropies as information-theoretic tools for complex network comparison},
  author={De Domenico, Manlio and Biamonte, Jacob},
  journal={Physical Review X},
  volume={6},
  number={4},
  pages={041062},
  year={2016},
  publisher={American Physical Society}
}

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License

This package is released under the MIT License.
See the LICENSE file for details.