RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 1,814,615
n graph size (no. of vertices) 866,599
dmax max degree 117,410
d+max max in-degree 117,410
d-max max out-degree 130
z mean total degree 4.188
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+.
275
h h-index, respecting total degree 275
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.
1,482
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.
1,813,133
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.
1
PR max pagerank value 0.005
Cd+ max in-degree centrality 0.135
Cd- max out-degree centrality 0
Cd max degree centrality 0.135
α powerlaw exponent, degree distribution 2.366
dminα dmin for α 82
α+ powerlaw exponent, in-degree distribution 2.348
dminα+ dmin for α+ 84
σ+ standard deviation, in-degree distribution 190.072
σ- standard deviation, out-degree distribution 2.307
cv+ coefficient variation, in-degree distribution 9,077.2
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 110.193
σ2+ variance, in-degree distribution 36,127.401
σ2- variance, out-degree distribution 5.324
C+d graph centralization 0.135
z- mean out-degree 3.941
$$deg^{--}(G)$$ max partial out-degree 126
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.05
$$deg^-_L(G)$$
Effective measure!Score: 0.099

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

max labelled out-degree 6
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 3.754
$$deg^-_D(G)$$ max direct out-degree 130
$$\overline{deg^-_D}(G)$$ mean direct out-degree 3.938
z+ mean in-degree 2.469
$$deg^{++}(G)$$ max partial in-degree 117,410
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.468
$$deg^+_L(G)$$ max labelled in-degree 2
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1
$$deg^+_D(G)$$ max direct in-degree 117,410
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.128

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

mean direct in-degree 2.467
$$deg_P(G)$$ max predicate degree 334,325
$$\overline{deg_P}(G)$$ mean predicate degree 151,217.917
$$deg^+_P(G)$$ max predicate in-degree 301,515
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 144,041.833
$$deg^-_P(G)$$ max predicate out-degree 184,045
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 61,259.75
$$\propto_{s-o}(G)$$ subject-object ratio 0.38
$$r_L(G)$$ 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 132,294
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.129

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

mean predicate list degree 3,009.451
$$C_G$$
Effective measure!Score: 0.06

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

distinct classes 5
$$S^C_G$$ all different typed subjects 301,515
$$r_T(G)$$ ratio of typed subjects 0.655

Plots

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