Requião da Cunha B,

PhD student - UFRGS

Brazilian Federal Police Agent

Fast Fragmentation of Networks Using Module-Based Attacks

http://dx.doi.org/10.1371/journal.pone.0142824

Gonçalves Sebastia,

Proffesor - UFRGS

González-Avella JC,

IFISC.

Data collection;

• Standardization of qualifiers.

Standardization of qualifiers.

CriminalN = 15.887

EmployN = 2038

FamiliarN = 8495

DoubtsN = 1040

LocalesN = 508

+ ++

++

Snapshot of organized Criminal groups investigated by the Brazilian Federal Police between April and August Of 2013

Snapshot of organized Criminal groups investigated by the Brazilian Federal Police between April and August Of 2013

Module-Based Attacks

Number of Nodes = 9888Number of links = 19744Avg path lenght = 14.43.Clustering Coeficient = 0.428Aveg. degree k= 3.99

Brazilian Criminal Network

Number of Nodes = 9888Number of links = 19744Avg path lenght = 14,43.Clustering Coeficient = 0.428Aveg. degree k= 3.99

Brazilian Criminal Network

Number of modules = 93

Q = 0.95821

Brazilian Criminal Inter-Comunity Network

Number of modules = 93

Inter-modules links = 176

Q = 0.95821

52-(35)-23

linksNodes = 196 Nodes = 77

9

Nodes = 183

(3 links)

52 [35] 2388 [27] 8686 [19] 2433 [13] 8630 [11] 2323 [11] 3121 [11] 6637 [10] 216 [10] 3721 [9] 8928 [8] 636 [8] 2174 [8] 2123 [8] 886 [7] 6721 [7] 9286 [7] 2886 [7] 7252 [6] 3052 [6] 42

28 [5] 4721 [5] 4179 [4] 706 [4] 6632 [4] 5479 [4] 8660 [4] 8652 [4] 3142 [4] 2338 [4] 9236 [3] 4763 [3] 3323 [3] 449 [3] 1524 [3] 8854 [3] 335 [3] 775 [3] 2344 [3] 499 [3] 52

21 [3] 4647 [3] 1415 [3] 219 [3] 438 [2] 317 [2] 3716 [2] 3250 [2] 1972 [2] 2415 [2] 3279 [2] 3385 [2] 1928 [2] 5411 [2] 6333 [2] 7070 [2] 8667 [2] 2482 [2] 2159 [2] 4221 [2] 2

32 [2] 233 [2] 7367 [2] 8815 [2] 4446 [2] 3754 [2] 8633 [2] 6252 [2] 817 [2] 1557 [2] 5491 [2] 659 [1] 3585 [1] 6719 [1] 2046 [1] 6886 [1] 4712 [1] 925 [1] 4915 [1] 333 [1] 2

32 [2] 233 [2] 7367 [2] 8815 [2] 4446 [2] 3754 [2] 8633 [2] 6252 [2] 817 [2] 1557 [2] 5491 [2] 659 [1] 3585 [1] 6719 [1] 2046 [1] 6886 [1] 4712 [1] 925 [1] 4915 [1] 333 [1] 2

Ci CjLink Ci CjLink Ci CjLink Ci CjLink Ci CjLink

Removed Links

Removed Nodes

Fig 2. Comparison between the effect of betweenness-based attack, degree-based attack, longest path attack, random attack, and module-based attack network.

Fig 4. Size of the biggest connected component in terms of the initial size, σ, as function of fraction of removed edges, ρ.

Fig 6. Overall efficiency gain (η) of the MBA method relative to the CBA method as function of modularity, Q, for nodes and edges removal.

The vertical axis is in logarithmic scale and the horizontal axis is linear. The networks attacked are Facebook (FB), Twitter (TW), Google Plus (G+), US power grid (PG), Euro road (ER), Open flights (OF), US airports (UA), Yeast protein (YP), H pylori (HP), and C elegans (CE).

Modularity and the fraction of bridging links.

Data Analisys Tools:

Python,NumpyScipyMatplotlibNetworkxCytoscapeR