94
Chapter 7. Modelling relationships that change over time
Period
1
2
3
4
5
6
7
8
9
10
11
Rank 1
N3
N1
N12
N12
N3
N1
N3
N12 N87 N40 N12
Rank 2
N1
N3
N3
N107
N12
N12
N12
N1
N14 N87 N76
Rank 3
N85 N76
N83
N3
N1
N14
N1
N14 N41 N37 N26
Rank 4
N89 N12
N1
N1
N107
N3
N14
N3
N37 N14 N43
Rank 5
N83 N85
N76
N83
N83
N76
N78
N22 N12 N12 N72
Rank 6
N6
N83
N86
N14
N14
N17
N76
N37
N1
N1
N41
Rank 7
N8
N9
N85
N89
N31
N107
N75
N76
N3
N82 N40
Rank 8
N5
N89
N13
N86
N89
N83
N85
N82 N76
N3
N87
Rank 9
N7
N5
N107
N63
N13
N85
N83
N87 N82 N83 N37
Rank 10
N2
N2
N9
N13
N86
N19
N107 N78 N22 N93
N1
Rank 11 N88
N6
N89
N85
N85
N13
N81
N33 N78 N22 N27
Rank 12 N54
N7
N2
N76
N76
N9
N13
N80 N16 N13
N3
Table 7.2: Individuals with the top 12 largest in-out edge lengths in each time period
of information of use to law enforcement: where relationships are strengthening or
weakening, and how apparent loyalties are shifting. In this particular dataset, the
reaction of the network to law enforcement actions (intercepting shipments) is also
detectable. Note especially that this analysis is done using only the existence of
calls between the members of the group, not the content of these calls. The cost of
collecting data on who called whom is orders of magnitude cheaper than collecting
content, but we have been able to show that essentially the same kinds of conclusions
about group operations and command and control can be drawn from the cheaper
data.
The other conclusion from this analysis is that criminal networks do not behave
like other kinds of social networks. Criminals do not introduce their friends to one
another; so there are many fewer triangles than expected; rather, the network looks
like a set of small stars, with occasional overlaps. Although there are detectable clusters, these are not tightly bound as they would be in a more typical social network,
but rather are loose aggregations around one or two figures.
7.3 Summary
Social networks change with time, as new members are added, current members
leave, and the strength of existing relationships increases or decreases. It is important
to be able to model these changes. Our layered approach enables time-varying social
networks to be bound into a single structure. Within this structure, comparisons can
be made rigorous, and the trajectories of individual nodes can be tracked against the
background of other nodes or clusters. When edges are directed, it also becomes
possible to draw conclusions about intentions because the individual or group at
the source end of a directed edge controls the weight on that edge. Increasing and
decreasing weights can therefore be ascribed to the desires or goals of the particular
nodes that control them.
Chapter 7. Modelling relationships that change over time
Period
1
2
3
4
5
6
7
8
9
10
11
Rank 1
N3
N1
N12
N12
N3
N1
N3
N12 N87 N40 N12
Rank 2
N1
N3
N3
N107
N12
N12
N12
N1
N14 N87 N76
Rank 3
N85 N76
N83
N3
N1
N14
N1
N14 N41 N37 N26
Rank 4
N89 N12
N1
N1
N107
N3
N14
N3
N37 N14 N43
Rank 5
N83 N85
N76
N83
N83
N76
N78
N22 N12 N12 N72
Rank 6
N6
N83
N86
N14
N14
N17
N76
N37
N1
N1
N41
Rank 7
N8
N9
N85
N89
N31
N107
N75
N76
N3
N82 N40
Rank 8
N5
N89
N13
N86
N89
N83
N85
N82 N76
N3
N87
Rank 9
N7
N5
N107
N63
N13
N85
N83
N87 N82 N83 N37
Rank 10
N2
N2
N9
N13
N86
N19
N107 N78 N22 N93
N1
Rank 11 N88
N6
N89
N85
N85
N13
N81
N33 N78 N22 N27
Rank 12 N54
N7
N2
N76
N76
N9
N13
N80 N16 N13
N3
Table 7.2: Individuals with the top 12 largest in-out edge lengths in each time period
of information of use to law enforcement: where relationships are strengthening or
weakening, and how apparent loyalties are shifting. In this particular dataset, the
reaction of the network to law enforcement actions (intercepting shipments) is also
detectable. Note especially that this analysis is done using only the existence of
calls between the members of the group, not the content of these calls. The cost of
collecting data on who called whom is orders of magnitude cheaper than collecting
content, but we have been able to show that essentially the same kinds of conclusions
about group operations and command and control can be drawn from the cheaper
data.
The other conclusion from this analysis is that criminal networks do not behave
like other kinds of social networks. Criminals do not introduce their friends to one
another; so there are many fewer triangles than expected; rather, the network looks
like a set of small stars, with occasional overlaps. Although there are detectable clusters, these are not tightly bound as they would be in a more typical social network,
but rather are loose aggregations around one or two figures.
7.3 Summary
Social networks change with time, as new members are added, current members
leave, and the strength of existing relationships increases or decreases. It is important
to be able to model these changes. Our layered approach enables time-varying social
networks to be bound into a single structure. Within this structure, comparisons can
be made rigorous, and the trajectories of individual nodes can be tracked against the
background of other nodes or clusters. When edges are directed, it also becomes
possible to draw conclusions about intentions because the individual or group at
the source end of a directed edge controls the weight on that edge. Increasing and
decreasing weights can therefore be ascribed to the desires or goals of the particular
nodes that control them.