Robustness of weighted networks

Bellingeri, Michele; Cassi, Davide

doi:10.1016/j.physa.2017.07.020

Cited by 57 publications

(87 citation statements)

References 37 publications

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“…The weighted betweenness centrality is computed using the weighted shortest paths that consider the number of links necessary to travel between nodes, but also consider the weight attached to the links. In this procedure, we first compute the inverse of the link weights, then we compute the weighted shortest paths as the minimum sum of the link weights necessary to travel among nodes 34,35 . The weighted betweenness centrality of a link accounts the number of weighted shortest paths from any couple of nodes (also called weighted geodesic) passing along that links 36 .…”

Section: Methodsmentioning

confidence: 99%

A comparative analysis of link removal strategies in real complex weighted networks

Bellingeri

Bevacqua²,

Scotognella

et al. 2020

Sci Rep

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In this report we offer the widest comparison of links removal (attack) strategies efficacy in impairing the robustness of six real-world complex weighted networks. We test eleven different link removal strategies by computing their impact on network robustness by means of using three different measures, i.e. the largest connected cluster (LCC), the efficiency (Eff) and the total flow (TF). We find that, in most of cases, the removal strategy based on the binary betweenness centrality of the links is the most efficient to disrupt the LCC. the link removal strategies based on binary-topological network features are less efficient in decreasing the weighted measures of the network robustness (e.g. Eff and TF). Removing highest weight links first is the best strategy to decrease the efficiency (Eff) in most of the networks. Last, we found that the removal of a very small fraction of links connecting higher strength nodes or of highest weight does not affect the LCC but it determines a rapid collapse of the network efficiency Eff and the total flow TF. this last outcome raises the importance of both to adopt weighted measures of network robustness and to focus the analyses on network response to few link removals. Understanding how the removal of nodes or links affects the functioning of a network is a major topic in science 1-6. It permits to rank nodes (or links) according to the consequence of their removal on the system. Also, it provides information for increasing the robustness (resilience) of networked systems 7,8. In fact, once the most important nodes-links are found, one can increase the network robustness by protecting these key components, for example by directing resources to preserve important internet routers or implementing policies to secure most important bridges (or roads) in transportation networks. For these reasons, many studies analysed the effect of removal (attack) strategies on real-world complex networks in different fields of science 1,2,9-17. Yet, recent classic outcomes indicated that many real-world complex networks showed 'robust yet fragile' nature, i.e. they are robust to the random removal of nodes but very fragile to the attack of the most connected node components 1,13,18,19. Following these outcomes, a plethora of attack strategies have been proposed to determine the sequence of nodes removal that maximise the damage in the networks 5,6,12,20-22. Most of these analyses consist in measuring the decrease in some indicators of the network integrity (functioning) following empirical removal of nodes-links 4-6,12,15,20-22. the link removal strategies. The main idea of link removal (also called link attack, link pruning or edge attack) strategies can be traced back to the Granovetter "The Strength of Weak Ties" 23 paper, that arguably contains the most influential sociological theory of networks. In this classic analysis the social interpersonal relationships were categorized in strong, weak or absent. A strong tie (link) is that one linking someone within a close circle of family and ...

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Section: Methodsmentioning

confidence: 99%

A comparative analysis of link removal strategies in real complex weighted networks

Bellingeri

Bevacqua²,

Scotognella

et al. 2020

Sci Rep

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“…Taking into consideration only the unweighted topology of the network would possibly lead, therefore, to erroneous conclusions about its robustness and capability to withstand an aggression or disruption. This aspect has been discussed in a recent paper by [34], whose framework inspired our analysis. To evaluate the effective impact of nodes removal, following [34], we also monitor the variation in the size of the Largest Connected Component (LCC) after every round of nodes removal.…”

Section: Robustnessmentioning

confidence: 94%

“…This aspect has been discussed in a recent paper by [34], whose framework inspired our analysis. To evaluate the effective impact of nodes removal, following [34], we also monitor the variation in the size of the Largest Connected Component (LCC) after every round of nodes removal. Finally, in line with [35], we also track the variation of the average local efficiency, which is an alternative indicator to the clustering coefficient in measuring the fault tolerance of disconnected networks [30,31].…”

Section: Robustnessmentioning

confidence: 94%

The evolving topology of the Lightning Network: Centralization, efficiency, robustness, synchronization, and anonymity

Martinazzi

Flori

2020

PLoS ONE

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The Lightning Network (LN) was released on Bitcoin's mainnet in January 2018 as a solution to favor scalability. This work analyses the evolution of the LN during its first year of existence in order to assess its impact over some of the core fundamentals of Bitcoin, such as: node centralization, resilience against attacks and disruptions, anonymity of users, autonomous coordination of its members. Using a network theory approach, we find that the LN represents a centralized configuration with few highly active nodes playing as hubs in that system. We show that the removal of these central nodes is likely to generate a remarkable drop in the LN's efficiency, while the network appears robust to random disruptions. In addition, we observe that improvements in efficiency during the sample period are primarily due to the increase in the capacity installed on the channels, while nodes' synchronization does not emerge as a distinctive feature of the LN. Finally, the analysis of the structure of the network suggests a good preservation of nodes' identity against attackers with prior knowledge about topological characteristics of their targets, but also that LN is probably weak against attackers that are within the system.

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“…Eff is a widely used measure of network functioning evaluating how efficiently the network exchanges information [20,48,49]. Eff is based on the shortest paths (SP) notion.…”

Section: The Network Efficiency (Eff)mentioning

confidence: 99%

“…the indegree (kin) and the number of outgoing links, the out-degree (kout). Nodes Strength (S): is the sum of the link weights to the nodes [49]. The strength of a node is the weighted counterpart of the node degree (k).…”

Section: The Psi Network Propertiesmentioning

confidence: 99%

Modeling the photosynthetic system I as complex interacting network

Montepietra

Bellingeri

Scotognella

et al. 2020

Preprint

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In this paper we model the excitation energy transfer (EET) of the photosynthetic system I (PSI) of the common pea plant Pisum Sativum as complex interacting network. The magnitude of the link energy transfer between nodes-chromophores is computed by Forster Resonant Energy Transfer (FRET) using the pairwise physical distances between chromophores from the PDB (Protein Data Bank). We measure the global PSI network EET efficiency adopting well-known network theory indicators: the network efficiency (Eff) and the largest connected component (LCC). We find that when progressively removing the weak links of lower EET, the network efficiency (Eff) decreases while the EET paths integrity (LCC) is still preserved. This finding would show that the PSI is a resilient system owning a large window of functioning feasibility and it is completely impaired only when removing most of the network links. Furthermore, we perform nodes removal simulations to understand how the nodes-chromophores malfunctioning may affect the PSI functioning. We discover that the removal of the core chlorophylls triggers the fastest decrease in the network efficiency (Eff), unveiling them as the key component boosting the high EET efficiency. Our outcomes open new perspectives of research, such comparing the PSI energy transfer efficiency of different natural and agricultural plant species and investigating the light-harvesting mechanisms of artificial photosynthesis both in plant agriculture and in the field of solar energy applications. Keywords: Complex network, photosystem I, photosynthetic network, biological network, network robustness, network attack.been directed to unveil the underneath structural and topological patterns shaping the high EET efficiency of the PSI system [2,3].The purpose of this research is the analysis of the structural organization of a plant PSΙ as a complex networked system for EET by means of network science viewpoint. Network science has proven to be a powerful tool for the study of complex systems from many different realms [18][19][20][21][22][23][24][25][26] . Basically, a network is a model composed by nodes (or vertices) and links (edges), where nodes indicate the components of the system and the links define the interactions among them [27,28] . Here we model the PSΙ light-harvesting system of the plant Pisum sativum as a complex network of nodeschromophores describing the energy transfer links among them. First, we find that the PSI is a highly connected network with very short EET pathways from the nodes harvesting the light to the RC.Second, we discover that the capacity to perform EET in the whole network is severely impaired only by removing the major amount of EET links. This unveils the high resilience of the PSI system, which holds the capacity to perform the energy transfer in the whole network even reaching severe conditions for its feasibility. Last, we simulate different scenarios of chromophores malfunctioning by removing nodes from the network [18,29]. We find that the removal towards the core Chl...

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Robustness of weighted networks

Cited by 57 publications

References 37 publications

A comparative analysis of link removal strategies in real complex weighted networks

A comparative analysis of link removal strategies in real complex weighted networks

The evolving topology of the Lightning Network: Centralization, efficiency, robustness, synchronization, and anonymity

Modeling the photosynthetic system I as complex interacting network

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