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) 194,892
n graph size (no. of vertices) 103,565
dmax max degree 32,482
d+max max in-degree 32,482
d-max max out-degree 6
z mean total degree 3.764
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+.
20
h h-index, respecting total degree 20
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.
0
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.
194,892
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 0.007
Cd+ max in-degree centrality 0.314
Cd- max out-degree centrality 0
Cd max degree centrality 0.314
α powerlaw exponent, degree distribution 34.042
dminα dmin for α 6
α+ powerlaw exponent, in-degree distribution 9.758
dminα+ dmin for α+ 1
σ+ standard deviation, in-degree distribution 174.822
σ- standard deviation, out-degree distribution 2.784
cv+ coefficient variation, in-degree distribution 9,289.98
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 147.932
σ2+ variance, in-degree distribution 30,562.666
σ2- variance, out-degree distribution 7.75
C+d graph centralization 0.314
z- mean out-degree 6
$$deg^{--}(G)$$ max partial out-degree 1
$$\overline{deg^{--}}(G)$$ 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 6
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 6
$$deg^-_D(G)$$ max direct out-degree 6
$$\overline{deg^-_D}(G)$$ mean direct out-degree 6
z+ mean in-degree 2.742
$$deg^{++}(G)$$ max partial in-degree 32,482
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.742
$$deg^+_L(G)$$ max labelled in-degree 1
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1
$$deg^+_D(G)$$ max direct in-degree 32,482
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.128

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

mean direct in-degree 2.742
$$deg_P(G)$$ max predicate degree 32,482
$$\overline{deg_P}(G)$$ mean predicate degree 32,482
$$deg^+_P(G)$$ max predicate in-degree 32,482
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 32,482
$$deg^-_P(G)$$ max predicate out-degree 32,482
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 11,847.167
$$\propto_{s-o}(G)$$ 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 32,482
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.129

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

mean predicate list degree 32,482
$$C_G$$
Effective measure!Score: 0.06

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

distinct classes 1
$$S^C_G$$ all different typed subjects 32,482
$$r_T(G)$$ 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