RDF Graph Measures for the Analysis of RDF Graphs

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Data and Resources

Measures

Notation Description Value
m graph volume (no. of edges) 44,381,726
n graph size (no. of vertices) 5,322,349
dmax max degree 3,997,078
d+max max in-degree 3,997,078
d-max max out-degree 520
z mean total degree 16.678
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+.
1,162
h h-index, respecting total degree 1,162
pmu fill, respecting unique edges only 0
p fill, respecting overall edges 0
mp
Effective measure!Score: 0.045

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

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.
2,232
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.
44,379,494
y reciprocity 0
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.
3
PR max pagerank value 0.009
Cd+ max in-degree centrality 0.751
Cd- max out-degree centrality 0
Cd max degree centrality 0.751
α powerlaw exponent, degree distribution 91.394
dminα dmin for α 12
α+ powerlaw exponent, in-degree distribution 2.857
dminα+ dmin for α+ 3
σ+ standard deviation, in-degree distribution 3,101.293
σ- standard deviation, out-degree distribution 4.88
cv+ coefficient variation, in-degree distribution 37,191.4
cv-
Effective measure!Score: 0.047

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

coefficient variation, out-degree distribution 58.52
σ2+ variance, in-degree distribution 9,618,019.223
σ2- variance, out-degree distribution 23.812
C+d graph centralization 0.751
z- mean out-degree 11.103
$$deg^{--}(G)$$ max partial out-degree 104
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1
$$deg^-_L(G)$$
Effective measure!Score: 0.099

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

max labelled out-degree 12
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 11.102
$$deg^-_D(G)$$ max direct out-degree 207
$$\overline{deg^-_D}(G)$$ mean direct out-degree 11.102
z+ mean in-degree 33.489
$$deg^{++}(G)$$ max partial in-degree 3,997,078
$$\overline{deg^{++}}(G)$$ mean partial in-degree 32.253
$$deg^+_L(G)$$ max labelled in-degree 4
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.038
$$deg^+_D(G)$$ max direct in-degree 3,997,078
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.128

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

mean direct in-degree 33.487
$$deg_P(G)$$ max predicate degree 3,998,111
$$\overline{deg_P}(G)$$ mean predicate degree 752,232.644
$$deg^+_P(G)$$ max predicate in-degree 3,997,297
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 752,179.373
$$deg^-_P(G)$$ max predicate out-degree 864,227
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 23,323.136
$$\propto_{s-o}(G)$$ subject-object ratio 0
$$r_L(G)$$ ratio of repreated predicate lists 1
$$deg_{PL}(G)$$
Effective measure!Score: 0.047

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

max predicate list degree 1,839,661
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.129

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

mean predicate list degree 249,831.125
$$C_G$$
Effective measure!Score: 0.06

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

distinct classes 7
$$S^C_G$$ all different typed subjects 3,997,297
$$r_T(G)$$ ratio of typed subjects 1

Plots

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