RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 153,933
n graph size (no. of vertices) 73,973
dmax max degree 4,960
d+max max in-degree 4,960
d-max
Effective measure!Score: 0.06

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

max out-degree 8
z mean total degree 4.162
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+.
72
h h-index, respecting total degree 72
pmu fill, respecting unique edges only 0
p fill, respecting overall edges 0
mp
Effective measure!Score: 0.09

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.
4,034
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.
149,899
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.
5
PR max pagerank value 0.006
Cd+ max in-degree centrality 0.067
Cd- max out-degree centrality 0
Cd max degree centrality 0.067
α powerlaw exponent, degree distribution 1.693
dminα dmin for α 20
α+ powerlaw exponent, in-degree distribution 2.208
dminα+ dmin for α+ 3
σ+ standard deviation, in-degree distribution 55.87
σ- standard deviation, out-degree distribution 2.385
cv+ coefficient variation, in-degree distribution 2,684.86
cv-
Effective measure!Score: 0.064

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

coefficient variation, out-degree distribution 114.626
σ2+ variance, in-degree distribution 3,121.474
σ2- variance, out-degree distribution 5.69
C+d graph centralization 0.067
z-
Effective measure!Score: 0.059

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

mean out-degree 3.799
$$deg^{--}(G)$$ max partial out-degree 2
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.033
$$deg^-_L(G)$$ max labelled out-degree 8
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 3.676
$$deg^-_D(G)$$ max direct out-degree 8
$$\overline{deg^-_D}(G)$$ mean direct out-degree 3.699
z+ mean in-degree 2.23
$$deg^{++}(G)$$ max partial in-degree 4,960
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.221
$$deg^+_L(G)$$ max labelled in-degree 4
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.004
$$deg^+_D(G)$$ max direct in-degree 4,960
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.066

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

mean direct in-degree 2.172
$$deg_P(G)$$ max predicate degree 39,566
$$\overline{deg_P}(G)$$ mean predicate degree 6,996.954
$$deg^+_P(G)$$ max predicate in-degree 39,566
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 6,771.454
$$deg^-_P(G)$$ max predicate out-degree 9,920
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 3,149.864
$$\propto_{s-o}(G)$$ subject-object ratio 0.481
$$r_L(G)$$ ratio of repreated predicate lists 1
$$deg_{PL}(G)$$ max predicate list degree 8,345
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.224

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

mean predicate list degree 3,117.154
$$C_G$$
Effective measure!Score: 0.046

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

distinct classes 8
$$S^C_G$$ all different typed subjects 39,566
$$r_T(G)$$ ratio of typed subjects 0.976

Plots

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