Maximising the clustering coefficient of networks and the effects on habitat network robustness.

The robustness of networks against node failure and the response of networks to node removal has been studied extensively for networks such as transportation networks, power grids, and food webs. In many cases, a network's clustering coefficient was identified as a good indicator for network ro...

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Main Authors: Henriette Heer, Lucas Streib, Ralf B Schäfer, Stefan Ruzika
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2020-01-01
Series:PLoS ONE
Online Access:https://doi.org/10.1371/journal.pone.0240940
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spelling doaj-ec1f52a2b76c4c519237c08c4d25a4a42021-03-04T11:09:40ZengPublic Library of Science (PLoS)PLoS ONE1932-62032020-01-011510e024094010.1371/journal.pone.0240940Maximising the clustering coefficient of networks and the effects on habitat network robustness.Henriette HeerLucas StreibRalf B SchäferStefan RuzikaThe robustness of networks against node failure and the response of networks to node removal has been studied extensively for networks such as transportation networks, power grids, and food webs. In many cases, a network's clustering coefficient was identified as a good indicator for network robustness. In ecology, habitat networks constitute a powerful tool to represent metapopulations or -communities, where nodes represent habitat patches and links indicate how these are connected. Current climate and land-use changes result in decline of habitat area and its connectivity and are thus the main drivers for the ongoing biodiversity loss. Conservation efforts are therefore needed to improve the connectivity and mitigate effects of habitat loss. Habitat loss can easily be modelled with the help of habitat networks and the question arises how to modify networks to obtain higher robustness. Here, we develop tools to identify which links should be added to a network to increase the robustness. We introduce two different heuristics, Greedy and Lazy Greedy, to maximize the clustering coefficient if multiple links can be added. We test these approaches and compare the results to the optimal solution for different generic networks including a variety of standard networks as well as spatially explicit landscape based habitat networks. In a last step, we simulate the robustness of habitat networks before and after adding multiple links and investigate the increase in robustness depending on both the number of added links and the heuristic used. We found that using our heuristics to add links to sparse networks such as habitat networks has a greater impact on the clustering coefficient compared to randomly adding links. The Greedy algorithm delivered optimal results in almost all cases when adding two links to the network. Furthermore, the robustness of networks increased with the number of additional links added using the Greedy or Lazy Greedy algorithm.https://doi.org/10.1371/journal.pone.0240940
collection DOAJ
language English
format Article
sources DOAJ
author Henriette Heer
Lucas Streib
Ralf B Schäfer
Stefan Ruzika
spellingShingle Henriette Heer
Lucas Streib
Ralf B Schäfer
Stefan Ruzika
Maximising the clustering coefficient of networks and the effects on habitat network robustness.
PLoS ONE
author_facet Henriette Heer
Lucas Streib
Ralf B Schäfer
Stefan Ruzika
author_sort Henriette Heer
title Maximising the clustering coefficient of networks and the effects on habitat network robustness.
title_short Maximising the clustering coefficient of networks and the effects on habitat network robustness.
title_full Maximising the clustering coefficient of networks and the effects on habitat network robustness.
title_fullStr Maximising the clustering coefficient of networks and the effects on habitat network robustness.
title_full_unstemmed Maximising the clustering coefficient of networks and the effects on habitat network robustness.
title_sort maximising the clustering coefficient of networks and the effects on habitat network robustness.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2020-01-01
description The robustness of networks against node failure and the response of networks to node removal has been studied extensively for networks such as transportation networks, power grids, and food webs. In many cases, a network's clustering coefficient was identified as a good indicator for network robustness. In ecology, habitat networks constitute a powerful tool to represent metapopulations or -communities, where nodes represent habitat patches and links indicate how these are connected. Current climate and land-use changes result in decline of habitat area and its connectivity and are thus the main drivers for the ongoing biodiversity loss. Conservation efforts are therefore needed to improve the connectivity and mitigate effects of habitat loss. Habitat loss can easily be modelled with the help of habitat networks and the question arises how to modify networks to obtain higher robustness. Here, we develop tools to identify which links should be added to a network to increase the robustness. We introduce two different heuristics, Greedy and Lazy Greedy, to maximize the clustering coefficient if multiple links can be added. We test these approaches and compare the results to the optimal solution for different generic networks including a variety of standard networks as well as spatially explicit landscape based habitat networks. In a last step, we simulate the robustness of habitat networks before and after adding multiple links and investigate the increase in robustness depending on both the number of added links and the heuristic used. We found that using our heuristics to add links to sparse networks such as habitat networks has a greater impact on the clustering coefficient compared to randomly adding links. The Greedy algorithm delivered optimal results in almost all cases when adding two links to the network. Furthermore, the robustness of networks increased with the number of additional links added using the Greedy or Lazy Greedy algorithm.
url https://doi.org/10.1371/journal.pone.0240940
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