Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness
It is often claimed that the entropy of a network’s degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configur...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/9/1182 |
| _version_ | 1827661251748036608 |
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| author | Chris Jones Karoline Wiesner |
| author_facet | Chris Jones Karoline Wiesner |
| author_sort | Chris Jones |
| collection | DOAJ |
| description | It is often claimed that the entropy of a network’s degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configured networks when no other network characteristics are specified. Furthermore, we show that, for networks of fixed expected degree that follow degree distributions of the same form, the degree distribution entropy is not indicative of robustness. By contrast, we show that the remaining degree entropy and robustness have a positive monotonic relationship and give an analytic expression for the remaining degree entropy of the log-normal distribution. We also show that degree-degree correlations are not by themselves indicative of a network’s robustness for real networks. We propose an adjustment to how mutual information is measured which better encapsulates structural properties related to robustness. |
| first_indexed | 2024-03-10T00:05:51Z |
| format | Article |
| id | doaj.art-049c76eb67a44c6d97c3ce9207525d49 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T00:05:51Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-049c76eb67a44c6d97c3ce9207525d492023-11-23T16:07:21ZengMDPI AGEntropy1099-43002022-08-01249118210.3390/e24091182Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network RobustnessChris Jones0Karoline Wiesner1School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UKInstitut für Physik und Astronomie, Universität Potsdam, Campus Golm, Haus 28, Karl-Liebknecht-Straße 24/25, Golm, 14476 Potsdam, GermanyIt is often claimed that the entropy of a network’s degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configured networks when no other network characteristics are specified. Furthermore, we show that, for networks of fixed expected degree that follow degree distributions of the same form, the degree distribution entropy is not indicative of robustness. By contrast, we show that the remaining degree entropy and robustness have a positive monotonic relationship and give an analytic expression for the remaining degree entropy of the log-normal distribution. We also show that degree-degree correlations are not by themselves indicative of a network’s robustness for real networks. We propose an adjustment to how mutual information is measured which better encapsulates structural properties related to robustness.https://www.mdpi.com/1099-4300/24/9/1182complex networksnetwork robustnessdegree distribution entropyremaining degree entropymutual information of networks |
| spellingShingle | Chris Jones Karoline Wiesner Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness Entropy complex networks network robustness degree distribution entropy remaining degree entropy mutual information of networks |
| title | Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness |
| title_full | Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness |
| title_fullStr | Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness |
| title_full_unstemmed | Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness |
| title_short | Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness |
| title_sort | clarifying how degree entropies and degree degree correlations relate to network robustness |
| topic | complex networks network robustness degree distribution entropy remaining degree entropy mutual information of networks |
| url | https://www.mdpi.com/1099-4300/24/9/1182 |
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