RDF Graph Measures for the Analysis of RDF Graphs

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universal-dependencies-treebank-czech-cac

Data and Resources

Measures

Notation Description Value
m graph volume (no. of edges) 110,830
n graph size (no. of vertices) 19,612
dmax max degree 10,900
d+max max in-degree 10,900
d-max
Effective measure!Score: 0.04

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

max out-degree 11
z mean total degree 11.3
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+.
115
h h-index, respecting total degree 115
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.
8,000
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.
102,830
y reciprocity 0.026
δ
Effective measure!Score: 0.237

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.
627
PR max pagerank value 0.009
Cd+ max in-degree centrality 0.556
Cd- max out-degree centrality 0.001
Cd max degree centrality 0.556
α powerlaw exponent, degree distribution 5.983
dminα dmin for α 11
α+ powerlaw exponent, in-degree distribution 2.603
dminα+ dmin for α+ 3
σ+ standard deviation, in-degree distribution 90.761
σ- standard deviation, out-degree distribution 4.996
cv+ coefficient variation, in-degree distribution 1,606.07
cv- coefficient variation, out-degree distribution 88.406
σ2+ variance, in-degree distribution 8,237.611
σ2- variance, out-degree distribution 24.959
C+d graph centralization 0.555
z-
Effective measure!Score: 0.174

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

mean out-degree 9.614
$$deg^{--}(G)$$
Effective measure!Score: 0.168

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

max partial out-degree 1
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1
$$deg^-_L(G)$$
Effective measure!Score: 0.098

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 9.614
$$deg^-_D(G)$$
Effective measure!Score: 0.037

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

max direct out-degree 11
$$\overline{deg^-_D}(G)$$ mean direct out-degree 8.92
z+ mean in-degree 5.767
$$deg^{++}(G)$$ max partial in-degree 10,900
$$\overline{deg^{++}}(G)$$ mean partial in-degree 4.445
$$deg^+_L(G)$$ max labelled in-degree 2
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.298
$$deg^+_D(G)$$ max direct in-degree 10,900
$$\overline{deg^+_D}(G)$$
Effective measure!Score: 0.045

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

mean direct in-degree 5.351
$$deg_P(G)$$ max predicate degree 11,528
$$\overline{deg_P}(G)$$ mean predicate degree 9,235.833
$$deg^+_P(G)$$ max predicate in-degree 11,528
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 9,235.833
$$deg^-_P(G)$$ max predicate out-degree 10,272
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 2,078
$$\propto_{s-o}(G)$$ subject-object ratio 0.568
$$r_L(G)$$ ratio of repreated predicate lists 0.999
$$deg_{PL}(G)$$ max predicate list degree 4,391
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 1,048
$$C_G$$ distinct classes 2
$$S^C_G$$ all different typed subjects 11,528
$$r_T(G)$$ 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