Clasificación de la sentencia en el proceso de

d.1 Citation Distributions

(a)Complete network (b)Without international case law

Figure 5:Cumulative frequency distribution of the number of citations

The degrees of random and theoretical network are distributed normally: edges connect to vertices at random, creating most vertices (at random) with an aver- age degree, and proportionally fewer vertices with higher or lower degrees. Real life networks, however, have been observed to follow a power law, in which there are many vertices with a low degree, and exponentially fewer vertices with higher degrees (Barabasi and Albert,1999;Newman,2010, 247). For judicial citation net- works, this has been confirmed inLupu and Voeten(2011,425-426) and for academic citation networks in, among others,Borgatti and Everett(1999) andBoerner, Maru and Goldstone(2004).

Figure 5 shows there is a power-law distribution similar to Lupu and Voeten (2011) in the complete ICC network, as well as in the network without international organizations. The network in this study conforms to this trend.

d.2 Edge Betweenness Dendogram Analysis

As explained in sectionC.2on page53, modularity in this study can best be assessed on the basis of edge betweenness. One of the main benefits of this calculation of modularity, is that the researcher can decide on the number of communities based on the empirical data, without bias beforehand (Newman,2010,384-385).

Figure6on the next page shows the decomposition of the network without inter- national organizations. It shows the isolation of22communities. The chosen and

Figure 6:Dendogram based on edge betweenness community detection

shown cut-off point is at the10th iteration, resulting in the outlined communities which are the same communities as in figure 3 on page 23. It is the most logical decomposition of the groups:

• The isolated communities to the right and left of the two central groups be- come isolated early in the iterative process;

• If the cut-off point is one step higher, there would remain isolated commu- nities and one subgroup composed of everything from Jean Pierre Bemba Gomboet al. to ES. This would have no substantive meaning;

• If the cut-off point is one step lower, the yellow community would leave SK isolated, while it could be part of a group with substantive meaning, hence lessening the explanatory power of the subdivision.

Based on the same edge betweenness-method, the complete network had almost no modularity. There are no clear communities, and as such, a further analysis and justification of the choice of communities through a dendogram is not necessary.

d.3 K-core Decomposition

The k-core of a vertex is the ‘maximal subset of vertices such that each is connected to at leastkothers in the subset’ (Newman,2010,195). Fork =1, all vertices belong to this subset, since all vertices are connected to at least 1 other vertex. For k =

some other vertices, that used to be connected to the removed vertices, and these are also removed. This is repeated until a subset remains in which all vertices are still connected to at least 4 other vertices. This is then the4-core of the network. The algorithm holds for each value ofk. The higher the k-core of a vertex, the more strongly it is embedded in the network. The lower, the more peripheral it is.

Figure7shows the k-core decomposition of the networks. The substantive mean- ing of the figure corroborates the findings in the main text: there is a strongly connected core composed of ICC case law and other international courts’ case law, while national legal systems form the periphery.

(a)Complete network (b)Without international case law

Figure 7:K-core decomposition: the numbers show the k-core of each vertex

d.4 Assortativity and Homophily

Assortative mixing (also called homophily) is the tendency of vertices to align more closely with like vertices than with unlike vertices. The opposite is called dissorta- tive mixing. It is an aspect of social life (Moody,2005) as well as citation networks: academic literature is more likely to cite other papers in the same field (Newman, 2010, 220) and judges are more likely to cite other judgments on the same topic (Busch,2007; Fowler et al.,2007;Shahabuddeen,2007). High assortativity is char- acteristic of a network in which there is a strongly connected core, and a looser connected periphery.

The complete ICC citation network has an assortativity of47.48% with the type equaling the type of jurisdiction (see sectionF.1 on page 64). 0% indicates a net- work with no edges between vertices of the same type, and100% a network with only edges between vertices of the same type. This finding corroborates again the interpretation that there is a strongly connected core in which vertices of typeICC are substantially more likely to connect to each other than to vertices of typeCNTRY.

d.5 Greedy Community Optimalization

(a)Reprint of figure3a _(b)Fast greedy cluster-communities

Figure 8:Communities based on the fast greedy cluster algorithm

A greedy algorithm finds a different community structure, with four communities (see figure 8). There are no isolated cases, and the modularity score is (against expectation, see sectionC.2on page53) slightly higher with34.62%. Both the higher modularity score and the differing communities are primarily due to the fact that all the weight of the edges needed to be removed for the greedy algorithm to work. The main take-away from this modularity score, then, is that it corroborates the finding in the primary analysis that there are significantly different communities within the ICC citation network. Another version of the greedy algorithm, based on label propagation (and suffering from the same flaws), results in a modularity score of37.41%, further confirming the main findings.