Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
C RIME AND T ERROR M ATHEMATICAL E XPLORATION AND M ODELING OF DARK N ETWORKS A. “Sasha” Gutfraind University of Texas at Austin
University of Waterloo 2011
A. “Sasha” Gutfraind
Crime and Terror
Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
N ETWORK S CIENCE
How did this network emerge? How is it structured? How does it change? Newman MEJ. “Physics of Networks”, Physics Today 2008. A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
U NIFYING I DEAS (1999-2001)
Distribution of node degrees. Newman MEJ, 2003.
Emerged through a “Preferential Attachment” process Highly-clustered with a many “small-world” shortcuts When attacked, it’s “robust [spokes] yet fragile [hubs]” A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
O UTLINE
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DARK N ETWORKS ARE D IFFERENT
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C ASCADE R ESILIENCE IN DARK N ETWORKS
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AGENT-BASED M ODEL OF BANNED R ADICAL G ROUPS
Key findings: Dark networks 6= Other complex networks Two flavors of dark networks: Designed and Spontaneous Open problems in formation and dynamics
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
A L -Q AIDA 2001
Xu, J. and Chen, “The topology of dark networks”, Comm. ACM, October 2008.
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
T HE 9/11 NETWORK AND FTP 38 36 37 34 33 35
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Krebs, “Mapping Networks of Terrorist Cells”, Connections 24(3), 2002; AG, “Optimizing topological cascade resilience based on the structure of terrorist networks,” PLoS ONE, 10.1371, 2010; A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
PARIS 1944
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
A BSTRACT M ODEL FOR D ESIGNING DARK N ETWORK Hypothesis: compartmentalization provides cascade resilience while maintaining performance Approach: Recreate the network design problem Optimal network G ∈ G maximizes a mix of Resilience R (G) Efficiency W (G)
Optimization problem over “design” space G:
max rR (G) + (1 − r )W (G) G∈G
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A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
C ASCADE I LLUSTRATION
τ τ
τ
Time 1
Time 2
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
R ESILIENCE AND E FFICIENCY Resilience to cascade of network
R (G ) = 1 −
1 n−1
E[extent of cascade that starts at a single node]
Efficiency (or Value) W (G) =
1
∑
n(n − 1) u ,v 6=u ∈V
1 d (u , v )
Fitness F (G) = rR (G) + (1 − r )W (G)
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
F ITNESS OF E MPIRICAL N ETWORKS (r = .51) 0.7
11M 9/11 CollabNet Email FTP Gnutella Internet AS
0.6
Fitness
0.5 0.4 0.3 0.2 0.1
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
P ERCOLATION T HEOREM T HEOREM Let G be a graph on n nodes with edges sampled independently with probability p. Then in the limit n → ∞ with probability→1 the graph is connected if p > logn n and disconnected otherwise.
F IGURE : Random graph with n = 50. (a) p = 0.02, (b) p = 0.05 Erdos, P and Renyi, A, “On the evolution of random graphs”, Pub. Math.Instit. Hungar.Acad. Sci 1960. A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
N ETWORK D ESIGNS Networks based on Erdos-Renyi (ER) random graph G(n, p) Networks based on Connected Stars design Others
A. “Sasha� Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
I MPORTANCE OF C ELLS (r = .51) 1.0
ConnCliques ConnStars Cliques Cycles ER Stars
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Fitness
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
AVERAGE D EGREE
ConnCliques ConnStars Cliques Cycles ER Stars
101
0.0
0.2
0.4
τ
0.6
0.8
F IGURE : r = .49
1.0
Avg Degree+1
Avg Degree+1
ConnCliques ConnStars Cliques Cycles ER Stars
102
102
101
100 0.0
0.2
0.4
τ
0.6
0.8
F IGURE : r = .51
Bifurcation around r = 0.5: maximize efficiency (high average degree) or resilience (low average degree) A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
E FFICIENT F RONTIER (τ = 0.4) 1.0
ConnCliques ConnStars Cliques Cycles ER Stars
Efficiency
0.8 0.6 0.4 0.2 0.00.0
0.2
0.4
0.6
Resilience
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
H OME - GROWN T ERROR C ELLS
Emerge spontaneously as radicals find one another and mobilize Most notorious cases: Madrid 2003-03-11 and London 2005-07-07 bombings Recent cases in Canada: 2006 “Toronto 18” plot Severe challenge to law enforcement! How do those networks emerge, despite the risk and the low density?
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S IZES OF U NDERGROUND C ELLS 0.7
Environmentalist Right-Wing Islamist
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Probability
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
R ANDOM I NTERSECTION G RAPHS D EFINITION [Sociological] Magnet is any place (physical or online) where new friendships can form (e.g. pub, pickup volleyball team, book club).
D EFINITION A Uniform Random Intersection Graph G(n, k , p) assigns each of the n nodes each of the k colours at random with probability p. An edge (i , j ) ∈ G iff i and j have at least one shared color.
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K1
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S ELF -A SSEMBLY OF T ERRORIST C ELLS
Genkin, AG: “How Do Terrorist Cells Self-Assemble”. Winner: best paper award American Sociological Association, 2008. A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S UMMARY OF F INDINGS
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
C ELL S IZE VS . M AGNETS
T HEOREM Let G(n, k , p) with k ≤ n. Then in the limit n → ∞ with probability→1 the graph is connected if and only if p > logk n . Fill, Scheinerman, Singer-Cohen: “Random intersection graphs when m = w (n)”. Rand. Struct. Algorithms, 16(2), 2000. A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S IZES OF U NDERGROUND C ELLS 0.6
Empirical Simulated 0.5
Probability
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
O PEN Q UESTIONS
Scaling is P (X ≥ x ) ∼ x 2.5 for a variety of regions. What drives this? How do networks heal after attacks? Clauset, A. et al “On the Frequency of Severe Terrorist Events”, Journal of Conflict Resolution, 51(1), 2007. A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S UMMARY Dark networks 6= Other complex networks Two flavors of dark networks: Designed and Spontaneous Open problems in formation and dynamics
agutfraind.research@gmail.com Thanks to Michael Genkin, Rick Durrett, Aric Hagberg A. “Sasha� Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
O PTIONAL S LIDES
Optional Slides
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
N ETWORK D ESIGNS I Multiple independent cells: Cliques, Cycles and Stars Cascade-proof edges (not shown) could provide connectivity
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
N ETWORK D ESIGNS II Erdos-Renyi (ER) random graph G(n, p) Connected Cliques Connected Stars
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
11M N ETWORK
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
I MPLICATIONS
Star-like features improve resilience For some network designs, efforts are best put improving efficiency not cascade resilience; for others the other way around. For terrorist networks, depending on their design and cascade recovery (r ), it might be possible to induce phase transitions where their fitness drops or tactics turn non-violent.
A. “Sasha� Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
R ESULTS ABOUT F ITNESS L EMMA 1 For a given design G, the fitness of the optimal configuration is a decreasing function of τ (cascade risk) and g (attenuation).
L EMMA 2 For a given design G, the fitness of the optimal configuration is a continuous function of r (the weight of resilience). Notes Lemma 1 for τ stems from “monotonicity” of cascades. Lemma 2 - a standard result in multi-objective optimization? Fitness need not be a continuous function of τ . A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
S OLUTION P ROCESS Huge solution space: Brute force is not an option: O (exp(c 2 logn n )) graphs on n nodes Optimal set could be too large to analyze
Solution idea: search the space of graph-generating programs Only a few parameters are enough to configuration a program Actual networks are similar: constructed through “protocols”
Solving the optimization problem Grid Search & Derivative-Free Optimization Procedure: “Design” + Configuration =⇒Instances of networks =⇒evaluation of resilience & efficiency Cascade extent is found by simulation
A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
R ESILIENCE R (G) OF O PTIMAL N ETWORKS
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ConnCliques ConnStars Cliques Cycles ER Stars 0.0
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F IGURE : r = .49
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ConnCliques ConnStars Cliques Cycles ER Stars 0.2
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Bifurcation around r = 0.5: optimize for resilience or for efficiency A. “Sasha” Gutfraind
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Dark Networks are Different Cascade Resilience in Dark Networks Agent-Based Model of Banned Radical Groups
E FFICIENCY W (G) OF O PTIMAL N ETWORKS
1.0
1.0
0.8
ConnCliques ConnStars Cliques Cycles ER Stars
0.6 0.4
Efficiency
Efficiency
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0.6 0.4 0.2
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C ELL SIZE k OF O PTIMAL N ETWORKS
ConnCliques ConnStars Cliques Cycles Stars
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PARAMETER p OF O PT. N ETWORKS
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ACCURACY OF O PTIMAL k
80
ConnCliques ConnStars Cliques Cycles Stars
70 60
ConnCliques ConnStars Cliques Cycles Stars
50 40
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40 30
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F ITNESS L ANDSCAPE FOR S TARS D ESIGN 1.0
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0.900
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0.700
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60
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at low g , hardest to optimize near r = 0.5 Stars is slightly biased towards maximizing resilience. A. “Sasha” Gutfraind
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B INARY & W EIGHTED R EPRESENTATION
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11M (binary) 11M (weighted) 9/11 (binary) 9/11 (weighted)
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