Efficiency of scale-free networks: error and attack tolerance

By Paolo Crucitti, Vito Latora, Massimo Marchiori, Andrea Rapisarda. 2002

492 citations recorded by the source corpus.

The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e., networks with power law P(k), are considered: (1) scale-free networks with no local clustering produced by the Barabasi–Albert model and (2) scale-free networks with high clustering properties as in the model by Klemm and Eguiluz, and their properties are compared to the properties of random graphs (exponential graphs). By using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network. We show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors. We find that, at variance with random graphs, scale-free networks display, both on a global and on a local scale, a high degree of error tolerance and an extreme vulnerability to attacks. In fact, the global and the local efficiency are unaffected by the failure of some randomly chosen nodes, though they are extremely sensitive to the removal of the few nodes which play a crucial role in maintaining the network's connectivity.

Subfields: Geometry and Topology, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d388d0f8dc0e67587b6bc0372ceee7370ec3d58a

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In Geometry and Topology

In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Attack Robustness and Centrality of Complex Networks (2013, background): “In related work, [11] studies the efficiency of networks under the removal of vertices uniformly at random or in decreasing order of their degree.”
Graph theoretical analysis of complex networks in the brain (2007, methodology): “Efficiency has been used to show that scale-free networks are very resistant to random errors, but quite sensitive to targeted attacks [49].”
Mining communities and their relationships in blogs: A study of online hate groups (2007, background): “Another measure related to average path length is the network’s global efficiency, which is defined as the average of the inverses of shortest path lengths over all pairs of nodes in a network (Crucitti et al., 2003).”
Robustness and resilience of complex networks (2024, unknown): “…the most common approach 70 involves percolation-related metrics, such as monitoring the size of the largest connected component (LCC) and stopping the attack once it has reached a given target size, although other network metrics such as efficiency 59,71 or nestedness 50,51,72 have been used.”
GAT: A Graph-Theoretical Analysis Toolbox for Analyzing Between-Group Differences in Large-Scale Structural and Functional Brain Networks (2012, background): “Several global metrics like size, path length, mean local and global efficiency as well as a number of nodal metrics like nodal degree and betweenness have been suggested in the literature for assessing random failure and targeted attack analysis [3,11,14,20,58].”
The application of graph theoretical analysis to complex networks in the brain. (2007, unknown): “At this time, only few measures are available for the analysis of weighted graphs (Latora and Marchiori, 2001; Crucitti et al., 2003; Newman, 2004; Park et al., 2004; Barrat et al., 2004; Barthelemy et al., 2005; Onnela et al., 2005).”