RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 7,494,823
n graph size (no. of vertices) 2,538,313
dmax max degree 673,000
d+max max in-degree 673,256
d-max max out-degree 1,066
z mean total degree 5.91
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+.
218
h h-index, respecting total degree 271
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.
14,468
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.
7,480,355
y reciprocity 0.255
δ
Effective measure!Score: 0.09

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.
2
PR max pagerank value 0.009
Cd+ max in-degree centrality 0.265
Cd- max out-degree centrality 0
Cd max degree centrality 0.265
α powerlaw exponent, degree distribution 2.806
dminα dmin for α 40
α+ powerlaw exponent, in-degree distribution 2.457
dminα+ dmin for α+ 25
σ+ standard deviation, in-degree distribution 769.027
σ- standard deviation, out-degree distribution 4.286
cv+ coefficient variation, in-degree distribution 26,045.1
cv- coefficient variation, out-degree distribution 145.171
σ2+ variance, in-degree distribution 591,402.689
σ2- variance, out-degree distribution 18.374
C+d graph centralization 0.265
z-
Effective measure!Score: 0.052

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

mean out-degree 5.243
$$deg^{--}(G)$$ max partial out-degree 1,047
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.146
$$deg^-_L(G)$$
Effective measure!Score: 0.055

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

max labelled out-degree 14
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 4.574
$$deg^-_D(G)$$
Effective measure!Score: 0.063

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

max direct out-degree 1,066
$$\overline{deg^-_D}(G)$$ mean direct out-degree 5.233
z+ mean in-degree 2.953
$$deg^{++}(G)$$ max partial in-degree 673,256
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.371
$$deg^+_L(G)$$ max labelled in-degree 5
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.245
$$deg^+_D(G)$$ max direct in-degree 673,256
$$\overline{deg^+_D}(G)$$ mean direct in-degree 2.947
$$deg_P(G)$$ max predicate degree 1,429,580
$$\overline{deg_P}(G)$$ mean predicate degree 340,673.773
$$deg^+_P(G)$$ max predicate in-degree 1,429,580
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 297,251.182
$$deg^-_P(G)$$ max predicate out-degree 676,099
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 143,662.954
$$\propto_{s-o}(G)$$ subject-object ratio 0.563
$$r_L(G)$$ ratio of repreated predicate lists 0.989
$$deg_{PL}(G)$$
Effective measure!Score: 0.062

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

max predicate list degree 673,256
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.231

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

mean predicate list degree 88.224
$$C_G$$
Effective measure!Score: 0.048

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

distinct classes 3
$$S^C_G$$ all different typed subjects 1,429,580
$$r_T(G)$$ ratio of typed subjects 1

Plots

Degree distribution shown here
In-degree distribution shown here
Last update of this page: 25 March 2020 13:38:39 CET