RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 3,476,977
n graph size (no. of vertices) 791,979
dmax max degree 358,000
d+max max in-degree 357,594
d-max max out-degree 461
z mean total degree 8.78
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+.
332
h h-index, respecting total degree 421
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.
14,899
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.
3,462,078
y reciprocity 0.211
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.
2
PR max pagerank value 0.009
Cd+ max in-degree centrality 0.452
Cd- max out-degree centrality 0.001
Cd max degree centrality 0.452
α powerlaw exponent, degree distribution 1.836
dminα dmin for α 685
α+ powerlaw exponent, in-degree distribution 1.816
dminα+ dmin for α+ 462
σ+ standard deviation, in-degree distribution 475.692
σ- standard deviation, out-degree distribution 7.727
cv+ coefficient variation, in-degree distribution 10,835.2
cv- coefficient variation, out-degree distribution 176.013
σ2+ variance, in-degree distribution 226,283.09
σ2- variance, out-degree distribution 59.713
C+d graph centralization 0.452
z- mean out-degree 7.184
$$deg^{--}(G)$$ max partial out-degree 459
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.135
$$deg^-_L(G)$$ max labelled out-degree 15
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 6.328
$$deg^-_D(G)$$ max direct out-degree 461
$$\overline{deg^-_D}(G)$$ mean direct out-degree 7.153
z+ mean in-degree 4.494
$$deg^{++}(G)$$ max partial in-degree 357,594
$$\overline{deg^{++}}(G)$$ mean partial in-degree 4.418
$$deg^+_L(G)$$ max labelled in-degree 5
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.017
$$deg^+_D(G)$$ max direct in-degree 357,594
$$\overline{deg^+_D}(G)$$ mean direct in-degree 4.474
$$deg_P(G)$$ max predicate degree 490,062
$$\overline{deg_P}(G)$$ mean predicate degree 119,895.759
$$deg^+_P(G)$$ max predicate in-degree 484,008
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 105,609.897
$$deg^-_P(G)$$ max predicate out-degree 357,594
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 27,135.034
$$\propto_{s-o}(G)$$ subject-object ratio 0.588
$$r_L(G)$$ ratio of repreated predicate lists 0.999
$$deg_{PL}(G)$$ max predicate list degree 342,530
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 1,290.688
$$C_G$$ distinct classes 13
$$S^C_G$$ all different typed subjects 484,008
$$r_T(G)$$ ratio of typed subjects 1

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Degree distribution shown here
In-degree distribution shown here
Last update of this page: 25 March 2020 13:38:38 CET