RDF Graph Measures for the Analysis of RDF Graphs

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deutsche-nationalbibliografie-dnb

Data and Resources

Measures

Notation Description Value
m graph volume (no. of edges) 226,448,726
n graph size (no. of vertices) 92,499,102
dmax max degree 10,264,011
d+max max in-degree 10,264,011
d-max max out-degree 754
z mean total degree 4.896
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+.
2,603
h h-index, respecting total degree 2,604
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.
6,236,567
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.
220,212,159
y reciprocity 0.01
δ
Effective measure!Score: 0.09

Datasets in this domain can be very well described by means of this particular measure.

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.
10
PR max pagerank value 0.001
Cd+ max in-degree centrality 0.111
Cd- max out-degree centrality 0
Cd max degree centrality 0.111
α powerlaw exponent, degree distribution 2.031
dminα dmin for α 77
α+ powerlaw exponent, in-degree distribution 2.018
dminα+ dmin for α+ 60
σ+ standard deviation, in-degree distribution 1,573.08
σ- standard deviation, out-degree distribution 6.466
cv+ coefficient variation, in-degree distribution 64,256.7
cv- coefficient variation, out-degree distribution 264.129
σ2+ variance, in-degree distribution 2,474,581.237
σ2- variance, out-degree distribution 41.812
C+d graph centralization 0.111
z-
Effective measure!Score: 0.052

Datasets in this domain can be very well described by means of this particular measure.

mean out-degree 15.495
$$deg^{--}(G)$$ max partial out-degree 735
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.143
$$deg^-_L(G)$$
Effective measure!Score: 0.055

Datasets in this domain can be very well described by means of this particular measure.

max labelled out-degree 35
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 13.558
$$deg^-_D(G)$$
Effective measure!Score: 0.063

Datasets in this domain can be very well described by means of this particular measure.

max direct out-degree 751
$$\overline{deg^-_D}(G)$$ mean direct out-degree 15.068
z+ mean in-degree 2.782
$$deg^{++}(G)$$ max partial in-degree 10,264,011
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.664
$$deg^+_L(G)$$ max labelled in-degree 13
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.044
$$deg^+_D(G)$$ max direct in-degree 10,264,010
$$\overline{deg^+_D}(G)$$ mean direct in-degree 2.705
$$deg_P(G)$$ max predicate degree 23,951,420
$$\overline{deg_P}(G)$$ mean predicate degree 1,143,680.434
$$deg^+_P(G)$$ max predicate in-degree 13,202,389
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 1,000,676.773
$$deg^-_P(G)$$ max predicate out-degree 23,745,483
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 429,321.52
$$\propto_{s-o}(G)$$ subject-object ratio 0.038
$$r_L(G)$$ ratio of repreated predicate lists 0.903
$$deg_{PL}(G)$$
Effective measure!Score: 0.062

Datasets in this domain can be very well described by means of this particular measure.

max predicate list degree 1,334,920
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.231

Datasets in this domain can be very well described by means of this particular measure.

mean predicate list degree 10.346
$$C_G$$
Effective measure!Score: 0.048

Datasets in this domain can be very well described by means of this particular measure.

distinct classes 11
$$S^C_G$$ all different typed subjects 12,732,494
$$r_T(G)$$ ratio of typed subjects 0.871

Plots

Degree distribution shown here
In-degree distribution shown here
Last update of this page: 25 March 2020 13:38:39 CET