Measures
| Notation | Description | Value |
|---|---|---|
| m | graph volume (no. of edges) | 161,749,815 |
| n | graph size (no. of vertices) | 48,318,259 |
| dmax | max degree | 17,800,000 |
| d+max | max in-degree | 17,753,266 |
| d-max | max out-degree | 185,417 |
| z | mean total degree | 6.7 |
| h+ |
h-index, respecting in-degree
Known from citation networks, this measure is an indicator for the importance of a vertex in the graph, similar to a centrality measure. A value of h means that for the number of h vertices the degree of these vertices is greater or equal to h. A high value of h could be an indicator for a "dense" graph and that its vertices are more "prestigious".
The value is computed by respecting the in-degree distribution of the graph, denoted as
h+. |
1,554 |
| h | h-index, respecting total degree | 1,745 |
| pmu | fill, respecting unique edges only | 0 |
| p | fill, respecting overall edges | 0 |
| mp |
parallel edges
Based on the measure
mu, this is the number of parallel edges, i.e., the total number of edges that share the same pair of source and target vertices. It is computed by subtracting mu from the total number of edges m, i.e. mp = m – mu. |
1,237,082 |
| mu |
unique edges
In RDF, a pair of subject and object resources may be described with more than one predicate. Hence, in the graphs, there may exist a fraction of all edges that share the same pair of (subject and object) vertices. The value for
mu represents the total number of edges without counting these multiple edges between a pair of vertices. |
160,512,733 |
| y | reciprocity | 0.308 |
| δ |
diameter (approximated)
The diameter is the longest shortest path between a pair of two vertices in the graph (as there can be more than one path for the pair of vertices). As this requires all possible paths to be computed, this is a very computational intensive measure.
We used the pseudo_diameter-algorithm provided by graph-tool, which is an approximation method for the diameter of the graph.
As the graph can have many components, this algorithm very often returns the value of 1. If this should be the case for this graph, we compute the diameter for the largest connecting component.
|
23 |
| PR | max pagerank value | 0.012 |
| Cd+ | max in-degree centrality | 0.367 |
| Cd- | max out-degree centrality | 0.004 |
| Cd | max degree centrality | 0.367 |
| α | powerlaw exponent, degree distribution | 2.352 |
| dminα | dmin for α | 101 |
| α+ | powerlaw exponent, in-degree distribution | 2.229 |
| dminα+ | dmin for α+ | 53 |
| σ+ | standard deviation, in-degree distribution | 2,761.542 |
| σ- | standard deviation, out-degree distribution | 28.02 |
| cv+ | coefficient variation, in-degree distribution | 82,493.4 |
| cv- | coefficient variation, out-degree distribution | 837.021 |
| σ2+ | variance, in-degree distribution | 7,626,111.263 |
| σ2- | variance, out-degree distribution | 785.122 |
| C+d | graph centralization | 0.367 |
| z- | mean out-degree | 6.12 |
| $$deg^{--}(G)$$ | max partial out-degree | 185,414 |
| $$\overline{deg^{--}}(G)$$ | mean partial out-degree | 1.186 |
| $$deg^-_L(G)$$ | max labelled out-degree | 13 |
| $$\overline{deg^-_L}(G)$$ | mean labelled out-degree | 5.158 |
| $$deg^-_D(G)$$ | max direct out-degree | 185,417 |
| $$\overline{deg^-_D}(G)$$ | mean direct out-degree | 6.073 |
| z+ | mean in-degree | 3.421 |
| $$deg^{++}(G)$$ | max partial in-degree | 17,753,266 |
| $$\overline{deg^{++}}(G)$$ | mean partial in-degree | 3 |
| $$deg^+_L(G)$$ | max labelled in-degree | 5 |
| $$\overline{deg^+_L}(G)$$ | mean labelled in-degree | 1.14 |
| $$deg^+_D(G)$$ | max direct in-degree | 17,753,266 |
| $$\overline{deg^+_D}(G)$$ | mean direct in-degree | 3.395 |
| $$deg_P(G)$$ | max predicate degree | 26,054,275 |
| $$\overline{deg_P}(G)$$ | mean predicate degree | 4,256,574.079 |
| $$deg^+_P(G)$$ | max predicate in-degree | 26,048,008 |
| $$\overline{deg^+_P}(G)$$ | mean predicate in-degree | 3,587,455.895 |
| $$deg^-_P(G)$$ | max predicate out-degree | 17,753,266 |
| $$\overline{deg^-_P}(G)$$ | mean predicate out-degree | 1,419,077.658 |
| $$\propto_{s-o}(G)$$ | subject-object ratio | 0.526 |
| $$r_L(G)$$ | ratio of repreated predicate lists | 0.998 |
| $$deg_{PL}(G)$$ | max predicate list degree | 8,301,087 |
| $$\overline{deg_{PL}}(G)$$ | mean predicate list degree | 447.269 |
| $$C_G$$ | distinct classes | 10 |
| $$S^C_G$$ | all different typed subjects | 26,048,008 |
| $$r_T(G)$$ | ratio of typed subjects | 0.986 |
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