7.2. Applications of temporal networks
85
7.2 Applications of temporal networks
We illustrate the power of these techniques by applying them to a real-world criminal network, for which some of the structures are already known by other means.
The Caviar network was a criminal network for hashish and cocaine importation centered in Montr´ eal. Electronic surveillance data was gathered during a 2-year (1994—
1996) investigation (known as Project Caviar) conducted by the Montr´ eal Police, the
Royal Canadian Mounted Police and law-enforcement agencies from several countries (England, Spain, Italy, Brazil, Paraguay and Colombia) [64]. In this case, the
suspects were not arrested until the end of the 2-year period, although there were
11 seizures (four hashish consignments and seven cocaine consignments). This data
gives us the chance to observe a real-world criminal network, particularly its evolution over time and its responses to law-enforcement actions.
The data describes electronically monitored telephone conversations among a
total of 105 participants in the criminal network. Edge weights are the number of
calls in each period. We begin by treating the edges as undirected.
Data was collected over 11 periods, corresponding to 2-month investigative
phases for which interception warrants had to be obtained afresh [64]. Each of these
11 periods is treated as a subnetwork, and its data becomes the adjacency matrix
describing a snapshot.
Because law enforcement had access to the content of the telephone calls, they
were able to identify 5 key participants [63], N1 (the principal coordinator for hashish
importation), N12 (the principal coordinator for cocaine importation), N3 (a partner
to N1 and an intermediary between N1 and N12), N76 (a key trafficker), and N87
(a key financial investor in various drug consignments). The 5 key participants are
the most active in the network. In the figures, these 5 key participants are often
highlighted.
Figure 7.1 shows the Laplacian embedding of the network as a whole, that is
adding together all of the undirected interactions of all participants over all 11 time
periods. Figure 7.2 shows the center area of Figure 7.1 omitting the edges since the
pairwise distances represent similarity whether or not an edge exists in the graph.
There are three main clusters: a central one containing N1 and N3; one slightly
below it containing N87; and one to the upper left containing N12. There are also
several extreme arms of individuals with weak connections to the network. Recall
that nodes embedded centrally are most significant, and those embedded extremally
are least significant.
7.2.1 The undirected network over time
We can also examine the evolution of the structures in the network. In this example,
we use these parameters for the model: α = 0.5, β = 0.3. Even though there are 105
participants, on average only 32.5 participants made or received a phone call in each
2-month period, the number varying between 15 and 42. The total edge weight of
the active nodes in each time period ranges from 1 to 453.
The global undirected temporal criminal network is shown in Figure 7.3. In
85
7.2 Applications of temporal networks
We illustrate the power of these techniques by applying them to a real-world criminal network, for which some of the structures are already known by other means.
The Caviar network was a criminal network for hashish and cocaine importation centered in Montr´ eal. Electronic surveillance data was gathered during a 2-year (1994—
1996) investigation (known as Project Caviar) conducted by the Montr´ eal Police, the
Royal Canadian Mounted Police and law-enforcement agencies from several countries (England, Spain, Italy, Brazil, Paraguay and Colombia) [64]. In this case, the
suspects were not arrested until the end of the 2-year period, although there were
11 seizures (four hashish consignments and seven cocaine consignments). This data
gives us the chance to observe a real-world criminal network, particularly its evolution over time and its responses to law-enforcement actions.
The data describes electronically monitored telephone conversations among a
total of 105 participants in the criminal network. Edge weights are the number of
calls in each period. We begin by treating the edges as undirected.
Data was collected over 11 periods, corresponding to 2-month investigative
phases for which interception warrants had to be obtained afresh [64]. Each of these
11 periods is treated as a subnetwork, and its data becomes the adjacency matrix
describing a snapshot.
Because law enforcement had access to the content of the telephone calls, they
were able to identify 5 key participants [63], N1 (the principal coordinator for hashish
importation), N12 (the principal coordinator for cocaine importation), N3 (a partner
to N1 and an intermediary between N1 and N12), N76 (a key trafficker), and N87
(a key financial investor in various drug consignments). The 5 key participants are
the most active in the network. In the figures, these 5 key participants are often
highlighted.
Figure 7.1 shows the Laplacian embedding of the network as a whole, that is
adding together all of the undirected interactions of all participants over all 11 time
periods. Figure 7.2 shows the center area of Figure 7.1 omitting the edges since the
pairwise distances represent similarity whether or not an edge exists in the graph.
There are three main clusters: a central one containing N1 and N3; one slightly
below it containing N87; and one to the upper left containing N12. There are also
several extreme arms of individuals with weak connections to the network. Recall
that nodes embedded centrally are most significant, and those embedded extremally
are least significant.
7.2.1 The undirected network over time
We can also examine the evolution of the structures in the network. In this example,
we use these parameters for the model: α = 0.5, β = 0.3. Even though there are 105
participants, on average only 32.5 participants made or received a phone call in each
2-month period, the number varying between 15 and 42. The total edge weight of
the active nodes in each time period ranges from 1 to 453.
The global undirected temporal criminal network is shown in Figure 7.3. In