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) 334,701
n graph size (no. of vertices) 117,504
dmax max degree 17,200
d+max max in-degree 17,147
d-max max out-degree 67
z mean total degree 5.7
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+.
70
h h-index, respecting total degree 71
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.
1
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.
334,700
y reciprocity 0
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 0.006
Cd+ max in-degree centrality 0.146
Cd- max out-degree centrality 0.001
Cd max degree centrality 0.146
α powerlaw exponent, degree distribution 4.307
dminα dmin for α 5
α+ powerlaw exponent, in-degree distribution 2.08
dminα+ dmin for α+ 6
σ+ standard deviation, in-degree distribution 100.799
σ- standard deviation, out-degree distribution 3.694
cv+ coefficient variation, in-degree distribution 3,538.78
cv- coefficient variation, out-degree distribution 129.68
σ2+ variance, in-degree distribution 10,160.52
σ2- variance, out-degree distribution 13.644
C+d graph centralization 0.146
z-
Effective measure!Score: 0.052

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

mean out-degree 4.4
$$deg^{--}(G)$$ max partial out-degree 50
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.14
$$deg^-_L(G)$$
Effective measure!Score: 0.055

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

max labelled out-degree 13
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 3.86
$$deg^-_D(G)$$
Effective measure!Score: 0.063

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

max direct out-degree 67
$$\overline{deg^-_D}(G)$$ mean direct out-degree 4.4
z+ mean in-degree 2.949
$$deg^{++}(G)$$ max partial in-degree 10,982
$$\overline{deg^{++}}(G)$$ mean partial in-degree 2.411
$$deg^+_L(G)$$ max labelled in-degree 3
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.223
$$deg^+_D(G)$$ max direct in-degree 17,147
$$\overline{deg^+_D}(G)$$ mean direct in-degree 2.949
$$deg_P(G)$$ max predicate degree 76,068
$$\overline{deg_P}(G)$$ mean predicate degree 11,953.607
$$deg^+_P(G)$$ max predicate in-degree 76,068
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 10,486.893
$$deg^-_P(G)$$ max predicate out-degree 37,694
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 4,957.536
$$\propto_{s-o}(G)$$ subject-object ratio 0.613
$$r_L(G)$$ ratio of repreated predicate lists 0.997
$$deg_{PL}(G)$$
Effective measure!Score: 0.062

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

max predicate list degree 22,242
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.231

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

mean predicate list degree 295.988
$$C_G$$
Effective measure!Score: 0.048

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

distinct classes 17
$$S^C_G$$ all different typed subjects 76,068
$$r_T(G)$$ 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