RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 3,816,657
n graph size (no. of vertices) 2,068,863
dmax max degree 372,114
d+max max in-degree 372,114
d-max max out-degree 41,798
z mean total degree 3.69
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+.
156
h h-index, respecting total degree 156
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.
205,376
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.
3,611,281
y reciprocity 0.022
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.
3
PR max pagerank value 0.003
Cd+ max in-degree centrality 0.18
Cd- max out-degree centrality 0.02
Cd max degree centrality 0.18
α powerlaw exponent, degree distribution 6.688
dminα dmin for α 36
α+ powerlaw exponent, in-degree distribution 2.112
dminα+ dmin for α+ 18
σ+ standard deviation, in-degree distribution 297.176
σ- standard deviation, out-degree distribution 41.42
cv+ coefficient variation, in-degree distribution 16,108.8
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 2,245.25
σ2+ variance, in-degree distribution 88,313.751
σ2- variance, out-degree distribution 1,715.659
C+d graph centralization 0.18
z-
Effective measure!Score: 0.096

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

mean out-degree 10.256
$$deg^{--}(G)$$
Effective measure!Score: 0.117

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

max partial out-degree 41,791
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.103
$$deg^-_L(G)$$
Effective measure!Score: 0.159

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

max labelled out-degree 39
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 9.296
$$deg^-_D(G)$$
Effective measure!Score: 0.042

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

max direct out-degree 62
$$\overline{deg^-_D}(G)$$ mean direct out-degree 9.704
z+ mean in-degree 1.845
$$deg^{++}(G)$$ max partial in-degree 372,114
$$\overline{deg^{++}}(G)$$ mean partial in-degree 1.802
$$deg^+_L(G)$$
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 1.024
$$deg^+_D(G)$$ max direct in-degree 372,114
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.055

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

mean direct in-degree 1.746
$$deg_P(G)$$ max predicate degree 581,117
$$\overline{deg_P}(G)$$ mean predicate degree 90,872.786
$$deg^+_P(G)$$ max predicate in-degree 372,133
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 82,363.333
$$deg^-_P(G)$$ max predicate out-degree 372,114
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 50,427.214
$$\propto_{s-o}(G)$$ subject-object ratio 0.18
$$r_L(G)$$ ratio of repreated predicate lists 0.957
$$deg_{PL}(G)$$ max predicate list degree 242,881
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 23.164
$$C_G$$ distinct classes 20
$$S^C_G$$ all different typed subjects 372,133
$$r_T(G)$$ 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