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The Topology of Covert
Conflict
Shishir Nagaraja, Ross Anderson
Cambridge University
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
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)
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
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
Naïve Defenses Don’t Work!
• Basic vertexorder attack –
network dead
after 2 rounds
• Random
replenishment –
3 rounds
• Scale-free
replenishment –
4 rounds
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
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
Next Evolution …
• Combine two
defensive
strategies –
yellow graph is
delegation plus
cliques
• Modern terror
network?
• 3rd-generation
music-sharing
network?
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?
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
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?