8.4. Applications of signed networks
111
However, as before, there are some differences among the Laplacian embeddings. For example, Node WINF 12 (Winifrid), a leader of the “Young Turks” group,
does not have any incident negative edges and should be placed close to the center in
the embedding. In the embedding of Figure 8.6(a), WINF 12 is the extremal node in
the upper group. In Figures 8.6(b) and Figure 8.6(c), WINF 12 is placed much closer
to other groups, as it should be. BONAVEN 5 is a loyalist with no negative incident
edges, so ir should be placed close to the center of the network. This is what happens
using L bns and L sns but not using L rw . The measures for the Sampson monastery
dataset, computed in three dimensions, are shown in Table 8.2.
AER ANR MER
L rw 0.49
0.47
0.53
L sns 0.46
0.50
0.48
L bns 0.45
0.46
0.50
Table 8.2: Ratios for the Sampson monastery network embeddings — smaller values
are better
L sns and L bns have better performance overall, except that the ANR values of
the L sns is slightly worse than the ANR values of the L rw . But this time L sns has a
lower value than L bns for the MER score. Based on the embeddings of the two small
datasets, our two proposed signed Laplacian embedding methods are better than the
signed Laplacian embedding methods in Kunegis et al. [48]. However, it is hard to
decide which one of the two is the best.
ACLED violent groups network
The ACLED (Armed Conflict Location & Event Data Project — acleddata.com), is
a dataset of political violence events in Africa from 1997 to the present. Subsets of
this dataset were converted to directed signed social networks as follows: each record
describes an attack by group A on group B, possibly with A assisted by some other
group C and group B assisted by some other group D. This record results in a negative
directed edge from A to B, and positive directed edges from C to A and/or from D to
B. Multiple attacks or collaborations increase the edge weights accordingly. There
can be (and are!) both positive and negative edges between the same pair of actors.
We select records involving 21 countries in North and West Africa and the incidents involving violent groups. We use the largest connected component of groups:
173 groups. (As expected, there are small sets of groups that interact only with one
another, and we ignore these.) Most edges in this network are negative: 62 groups
have only negative edges and some have only one negative edge. The subset has
previously been examined from a geographical perspective [106].
Figure 8.7 shows the embeddings in three dimensions. The L rw embedding
shows a strong bipartite structure, while the other two show a more complex structure.
111
However, as before, there are some differences among the Laplacian embeddings. For example, Node WINF 12 (Winifrid), a leader of the “Young Turks” group,
does not have any incident negative edges and should be placed close to the center in
the embedding. In the embedding of Figure 8.6(a), WINF 12 is the extremal node in
the upper group. In Figures 8.6(b) and Figure 8.6(c), WINF 12 is placed much closer
to other groups, as it should be. BONAVEN 5 is a loyalist with no negative incident
edges, so ir should be placed close to the center of the network. This is what happens
using L bns and L sns but not using L rw . The measures for the Sampson monastery
dataset, computed in three dimensions, are shown in Table 8.2.
AER ANR MER
L rw 0.49
0.47
0.53
L sns 0.46
0.50
0.48
L bns 0.45
0.46
0.50
Table 8.2: Ratios for the Sampson monastery network embeddings — smaller values
are better
L sns and L bns have better performance overall, except that the ANR values of
the L sns is slightly worse than the ANR values of the L rw . But this time L sns has a
lower value than L bns for the MER score. Based on the embeddings of the two small
datasets, our two proposed signed Laplacian embedding methods are better than the
signed Laplacian embedding methods in Kunegis et al. [48]. However, it is hard to
decide which one of the two is the best.
ACLED violent groups network
The ACLED (Armed Conflict Location & Event Data Project — acleddata.com), is
a dataset of political violence events in Africa from 1997 to the present. Subsets of
this dataset were converted to directed signed social networks as follows: each record
describes an attack by group A on group B, possibly with A assisted by some other
group C and group B assisted by some other group D. This record results in a negative
directed edge from A to B, and positive directed edges from C to A and/or from D to
B. Multiple attacks or collaborations increase the edge weights accordingly. There
can be (and are!) both positive and negative edges between the same pair of actors.
We select records involving 21 countries in North and West Africa and the incidents involving violent groups. We use the largest connected component of groups:
173 groups. (As expected, there are small sets of groups that interact only with one
another, and we ignore these.) Most edges in this network are negative: 62 groups
have only negative edges and some have only one negative edge. The subset has
previously been examined from a geographical perspective [106].
Figure 8.7 shows the embeddings in three dimensions. The L rw embedding
shows a strong bipartite structure, while the other two show a more complex structure.