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) 9,539
n graph size (no. of vertices) 6,343
dmax max degree 716
d+max max in-degree 716
d-max max out-degree 132
z mean total degree 3.008
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+.
23
h h-index, respecting total degree 41
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.
140
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.
9,399
y reciprocity 0.002
δ
Effective measure!Score: 0.08

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.
1
PR max pagerank value 0.001
Cd+ max in-degree centrality 0.113
Cd- max out-degree centrality 0.021
Cd max degree centrality 0.113
α powerlaw exponent, degree distribution 2.977
dminα dmin for α 8
α+ powerlaw exponent, in-degree distribution 2.144
dminα+ dmin for α+ 13
σ+ standard deviation, in-degree distribution 12.906
σ- standard deviation, out-degree distribution 6.075
cv+ coefficient variation, in-degree distribution 858.212
cv- coefficient variation, out-degree distribution 403.938
σ2+ variance, in-degree distribution 166.574
σ2- variance, out-degree distribution 36.902
C+d graph centralization 0.112
z-
Effective measure!Score: 0.055

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

mean out-degree 13.416
$$deg^{--}(G)$$ max partial out-degree 108
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.714
$$deg^-_L(G)$$
Effective measure!Score: 0.062

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

max labelled out-degree 11
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 7.827
$$deg^-_D(G)$$
Effective measure!Score: 0.082

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

max direct out-degree 128
$$\overline{deg^-_D}(G)$$ mean direct out-degree 13.219
z+ mean in-degree 1.681
$$deg^{++}(G)$$ max partial in-degree 716
$$\overline{deg^{++}}(G)$$ mean partial in-degree 1.63
$$deg^+_L(G)$$
Effective measure!Score: 0.08

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

max labelled in-degree 2
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.031
$$deg^+_D(G)$$ max direct in-degree 711
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.057

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

mean direct in-degree 1.656
$$deg_P(G)$$ max predicate degree 2,401
$$\overline{deg_P}(G)$$ mean predicate degree 733.769
$$deg^+_P(G)$$ max predicate in-degree 711
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 428.077
$$deg^-_P(G)$$ max predicate out-degree 2,329
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 450.077
$$\propto_{s-o}(G)$$ subject-object ratio 0.007
$$r_L(G)$$ ratio of repreated predicate lists 0.684
$$deg_{PL}(G)$$ max predicate list degree 82
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 3.16
$$C_G$$
Effective measure!Score: 0.168

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 711
$$r_T(G)$$ ratio of typed subjects 1

Plots

Degree distribution shown here
In-degree distribution shown here
Last update of this page: 25 March 2020 13:38:37 CET