RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 7,033,740
n graph size (no. of vertices) 2,856,587
dmax max degree 488,138
d+max max in-degree 488,136
d-max max out-degree 167,681
z mean total degree 4.925
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+.
379
h h-index, respecting total degree 401
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.
945,365
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.
6,088,375
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.
4
PR max pagerank value 0.002
Cd+ max in-degree centrality 0.171
Cd- max out-degree centrality 0.059
Cd max degree centrality 0.171
α powerlaw exponent, degree distribution 2.302
dminα dmin for α 64
α+ powerlaw exponent, in-degree distribution 1.991
dminα+ dmin for α+ 24
σ+ standard deviation, in-degree distribution 560.562
σ- standard deviation, out-degree distribution 147.355
cv+ coefficient variation, in-degree distribution 22,765.9
cv-
Effective measure!Score: 0.256

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

coefficient variation, out-degree distribution 5,984.46
σ2+ variance, in-degree distribution 314,229.277
σ2- variance, out-degree distribution 21,713.365
C+d graph centralization 0.171
z-
Effective measure!Score: 0.096

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

mean out-degree 14.409
$$deg^{--}(G)$$
Effective measure!Score: 0.117

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

max partial out-degree 167,674
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.323
$$deg^-_L(G)$$
Effective measure!Score: 0.159

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

max labelled out-degree 25
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 10.893
$$deg^-_D(G)$$
Effective measure!Score: 0.042

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

max direct out-degree 234
$$\overline{deg^-_D}(G)$$ mean direct out-degree 12.472
z+ mean in-degree 2.535
$$deg^{++}(G)$$ max partial in-degree 488,136
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.454
$$deg^+_L(G)$$
Effective measure!Score: 0.08

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

max labelled in-degree 4
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.033
$$deg^+_D(G)$$ max direct in-degree 488,136
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.055

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

mean direct in-degree 2.194
$$deg_P(G)$$ max predicate degree 1,464,326
$$\overline{deg_P}(G)$$ mean predicate degree 260,508.889
$$deg^+_P(G)$$ max predicate in-degree 488,142
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 196,937.926
$$deg^-_P(G)$$ max predicate out-degree 488,136
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 106,134.333
$$\propto_{s-o}(G)$$ subject-object ratio 0.142
$$r_L(G)$$ ratio of repreated predicate lists 0.995
$$deg_{PL}(G)$$ max predicate list degree 210,738
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 209.323
$$C_G$$ distinct classes 16
$$S^C_G$$ all different typed subjects 488,142
$$r_T(G)$$ 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