The heterogeneity in link weights may decrease the robustness of real-world complex weighted networks

Abstract

Here we report a comprehensive analysis of the robustness of seven high-quality real-world complex weighted networks to errors and attacks toward nodes and links. We use measures of the network damage conceived for a binary (e.g. largest connected cluster LCC , and binary efficiency Eff bin ) or a weighted network structure (e.g. the efficiency Eff , and the total flow TF ). We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. These findings unveil a problematic response-state where the attack toward a small fraction of nodes-links returns the real-world complex networks in a connected but inefficient state . Our findings unveil how the robustness may be overestimated when focusing on the connectedness of the components only. Last, to understand how the networks robustness is affected by link weights heterogeneity, we randomly assign link weights over the topological structure of the real-world networks and we find that highly heterogeneous networks show a faster efficiency decrease under nodes-links removal: i.e. the robustness of the real-world complex networks against nodes-links removal is negatively correlated with link weights heterogeneity.

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

“…• Strong: links are removed in decreasing order of weight, i.e. links with higher weight are removed first 3,28,30 and it represents an attack directed to strong links. • Weak: links are deleted in increasing order of weight, i.e.…”

“…The total flow (TF). The total flow represents the actual or the potential flowing in the network 30 and it is the sum of link weights. Let be the weighted network G w, it can be represented by a N × N matrix W where the element w ij > 0 if there is a link of weight w between nodes i and j,and w ij = 0 otherwise.…”

“…In our analyses we adopted the weighted version of the efficiency metric with d(i,j) representing the weighted shortest path between node i and node j. To calculate the weighted shortest paths, we first applied a standard procedure by computing the inverse of the link weights 30,34,35 . This standard procedure has the aim to consider 'shorter and wider routes' the links of higher weight and 'longer and narrow routes' the links of lower weight.…”

Modeling the photosynthetic system I as complex interacting network

“…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.…”

“…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]…”