1. 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

2. 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).

3. 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

4. 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

5. 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

6. 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

7. 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

8. Attack Strategies: Dynamical Importance

9. Results

11. 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.

12. 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.

13. 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.

14. Attack Strategies