The Impact of Imperfect Information on Network Attack

Andrew Melchionna (University of Rochester)

Jesús Caloca (Boise State University)Advisors: S. Squires, M. Girvan, E. Ott, T. Antonsen

What is a network? A network represents connections

(links) between system components (nodes)

Examples include social networks (friendships), the Internet, and neural networks

In many cases, the network data we have contains errors (e.g. Facebook links may not accurately reflect true friendships).

Attacking the Giant Connected Component

Connected Component: group of nodes connected via some paths of edges

Our goal: remove nodes from (‘attack’) the network in order to break up Giant Connected Component (GCC)

The catch: the info we have about the network contains errors (false and missing links)

While attacks on networks have been studied previously, our focus of the effect of imperfect information on attack is new

Applications: include vaccinating to stop an epidemic, stopping terrorist communication

Simulating Imperfect Information about Network Links

We create a noisy network from the true network in which some false links are added and/or some true links are missing

Attack Strategies Nodes are removed in order of a specific "centrality" measure,

meant to capture how influential each node is in the network After each removal, we check the GCC size of the true network and

use the noisy network to recalculate new centrality measures for each node in the network

Centrality measures for attack strategies include:− Degree− Betweenness− Dynamical Importance

Attack Strategies: Degree Centrality

A node’s degree is the number of links attached to it An attack based on degree centrality removes the highest-

degree nodes first

Attack Strategies: Betweenness Centrality

The betweenness of a node considers the shortest paths between all pairs of nodes, and is proportional to the number of shortest paths that pass through the node

Attack Strategies:Dynamical Importance

The dynamical importance of a node is determined from the N x N (where N = # of nodes) network adjacency matrix: if there is a link from node i to node j and otherwise. The dynamical importance of a node is the change in the largest eigenvalue of the matrix after the node’s removal.

Unlike the degree centrality, which is a purely local centrality measure, the dynamical importance takes into account global information in the network for the influence of the node.

ResultsTrue networks haveN = 2,500 Nodes, M 10,000 links, data averaged over 50 realizations

Noisy networks have 2,500 links missing and 2,500 false links.

Results

Conclusions

The more sophisticated attack strategies remain effective even when the network information contains a significant number of link errors.

The effectiveness of attack strategies is more robust to the addition of false links compared with the deletion of true links.

We have also obtained results for other types of networks, for which find that the above conclusions also apply.

Acknowledgements Thanks to Dr. Shane Squires and Profs. Girvan, Ott and

Antonsen TREND Program and the University of Maryland National Science Foundation Jesús acknowledges the support of the McNair Scholars

Program.

References

Albert, R., H. Jeong, and A.L. Barabasi, "Error and attack tolerance of complex networks," Nature 406 (2000) 378-382.

Restrepo, J. G., E. Ott, and B. R. Hunt. “Characterizing the dynamical importance of network nodes and links." Physical Review Letters 97.9 (2006): 094102.

Platig, J., E. Ott, and M. Girvan. "Robustness of network measures to link errors." Physical Review E 88.6 (2013): 062812.