What Is the Entropy of a Social Organization?
Abstract
:1. Introduction
2. Quantifying the Potentiality of a Social Organization
2.1. Network Representation of a Social Organization
2.2. Potentiality of a Social Organization
2.2.1. Potentiality and Constraints
2.2.2. How to Proxy Constraints
2.2.3. Network Ensembles and Their Probability Distribution
3. Introducing the Generalized Hypergeometric Ensembles
3.1. Obtaining
3.1.1. Parameters of a gHypEG
3.1.2. Calculating for Networks
3.1.3. Calculating for Networks
3.2. Tractability of the Entropy
3.2.1. Multinomial Entropy Approximation
3.2.2. Computing the Multinomial Entropy
3.3. Comparing Entropy Values
Normalizing Value Ranges
3.4. Examples for
3.4.1. Two Special Cases
3.4.2. Complete Network
3.4.3. Star Network
4. Applications to Real-World Datasets
4.1. Examined Datasets
4.1.1. Southern Women Dataset
4.1.2. Karate Club Dataset
4.1.3. Conference Dataset
4.1.4. Network Overview
4.2. Potentiality of the Empirical Networks
4.2.1. Southern Women Network
4.2.2. Karate Club Network
4.2.3. Conference Networks
5. Conclusions
5.1. Fixed Numbers of Nodes and Edges
5.2. Large Number of Degrees of Freedom
5.3. Computability
Author Contributions
Funding
Conflicts of Interest
Appendix A. Fitting the Ξ Matrix for Undirected Networks Without Self-Loops
Appendix B. Convergence in Distribution of gHypEGs
Appendix C. Full Matrices for the Complete and the Star Network
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Network | n | m | D | |||
---|---|---|---|---|---|---|
Southern Women | 18 | 322 | ||||
Karate Club | 34 | 231 | ||||
Conference | 113 | 6925 | ||||
Conference | 113 | 7131 | ||||
Conference | 113 | 6762 |
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Zingg, C.; Casiraghi, G.; Vaccario, G.; Schweitzer, F. What Is the Entropy of a Social Organization? Entropy 2019, 21, 901. https://doi.org/10.3390/e21090901
Zingg C, Casiraghi G, Vaccario G, Schweitzer F. What Is the Entropy of a Social Organization? Entropy. 2019; 21(9):901. https://doi.org/10.3390/e21090901
Chicago/Turabian StyleZingg, Christian, Giona Casiraghi, Giacomo Vaccario, and Frank Schweitzer. 2019. "What Is the Entropy of a Social Organization?" Entropy 21, no. 9: 901. https://doi.org/10.3390/e21090901