1. The Topology of Covert Conflict Shishir Nagaraja, Ross Anderson Cambridge University

2. Topology and Resilience Many real-world networks can be modeled as scale-free – social contacts, disease spread, spread of computer viruses Power-law distribution of vertex order, often arising from preferential attachment Highly-connected nodes greatly enhance connectivity This gives resilience against random failure

3. Topology and Vulnerability Although power-law vertex order distribution gives resilience to random failure, it makes the network vulnerable to targeted attack If you attack high-order nodes, the network is rapidly disconnected (Albert, Jeong and Barabási, 2000) Example: Sierra Leone HIV/AIDS program treated prostitutes first – only 2% of population infected (vs 40% in Botswana)

4. Topology and Vulnerability (2) Music companies target high-order nodes in peer-to-peer networks (prolific uploaders) More traditional example: if you conquer a country, subvert or kill the bourgeoisie first What about the dynamic case, e.g. insurgency? Police keep arresting, insurgents keep recruiting We set out to study this dynamic case, using evolutionary game theory

5. Simulation Methodology After Axelrod’s work on iterated prisoners’ dilemma Scale-free network of 400 nodes At each round, attacker kills 10 nodes – their selection is his strategy Defender recruits 10 more, then reconfigures network – how he does this is his strategy Iterate search for defense, attack strategy

6. Naïve Defenses Don’t Work! Basic vertex- order attack – network dead after 2 rounds Random replenishment – 3 rounds Scale-free replenishment – 4 rounds

7. Evolving Defense Strategies Black – scalefree replenishment Green – replace high-order nodes with rings Cyan - replace high-order nodes with cliques Cliques work very well against the vertex-order attack

8. Evolving Attack Strategies Centrality attacks are the best counter we found to clique-based defenses Rings: G, B cliques: C, M Vertex-order attack: B, G, C Attack using centrality: R, B, M

9. Next Evolution … Combine two defensive strategies – yellow graph is delegation plus cliques Modern terror network? 3rd-generation music-sharing network?

10. What this teaches People set out to make peer-to-peer systems robust by arranging the nodes in rings. This didn’t work. Clubs do work We have some insight into why insurgents organise themselves in cells We can model strategies for wiretapping, surveillance, counterinsurgency … What about biology?

11. Biological Robustness Redundancy via homologous genes makes an organism better able to evolve (phenotypic changes less often lethal) This evolvability is an important element of robustness (Hiroaki Kitano, Nature, Nov 2004, pp 826–837) What we call ‘cells’ biologists think of as conserved clusters, the bows in bow-tie networks, or evolutionary capacitors Our work may give an insight into the evolution of hierarchical modularity

12. Conclusion We’ve built a bridge between network analysis and evolutionary game theory Using our simulation methodology, we get insights into why revolutionaries use cells, the effects of modern policing, and more Simulations let us explore many new attack and defense strategies Implications for all sorts of networks – computer, social, political … biological?