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

Abstract

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 ...

Link and Node Removal in Real Social Networks: A Review

“…The binary network approach has the advantages of simplicity and low computational cost and is straight-forward in gathering information to describe the network. Nonetheless, recent analyses showed that a thorough description of real networks should consider the heterogeneity of the links-interactions [34][35][36][37]. In fact, almost all real networks are characterized by links with different "weights" indicating the strength of the interaction among nodes.…”

“…Even in this case, the LCC is not able to evaluate the network functioning decrease, probably underestimating its damage. For these reasons, even when adopted in weighted networks, the LCC returns a pure topological description, neglecting to evaluate the underlying weighted structure [34][35][36][37].…”

“…Eff decreases with an increase in the nodes' shortest paths, thus defining as a more efficient networks with closer nodes. Eff performs a more granular evaluation of the network functioning after LNR by considering the elongation of shortest paths when the nodes are still connected ( Figures 1A,B) and by giving more importance to the removal of strong links that play a major role in routing the shortest paths and the system spreading capacity [37,49]. We remark that spreading is a dynamic process and that LCC and Eff are "static" indicators summarizing in a single value the extent of dynamic processes occurring in networks.…”

Modeling the photosynthetic system I as complex interacting network

“…Differently, the weighted shortest paths (wSP) consider both the number of links and the weight attached to them. To compute wSP, we first compute the inverse of the link weights; then we compute the weighted shortest paths as the minimum sum of the inverse link weights necessary to travel among nodes [27,34] .…”

“…We find that the removal towards the core Chls is clearly more harmful in decreasing the PSI functioning, suggesting the core as the key structural component of the high efficiency EET in the PSI of the P. Sativum.where the element wi,j>0 in the case there is link of weight wi,j between the node i and the node j and wi,j=0 otherwise. Many empirical researches demonstrate that purely binary-topological models are inadequate to explain the complex structure of the real systems, and that there is a need for weighted network models to overcome the pure topological description [27,28,34]…”