RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 22,830
n graph size (no. of vertices) 7,160
dmax max degree 3,710
d+max max in-degree 3,708
d-max max out-degree 211
z mean total degree 6.38
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+.
15
h h-index, respecting total degree 22
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.
8,217
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.
14,613
y reciprocity 0.001
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.
1
PR max pagerank value 0.013
Cd+ max in-degree centrality 0.518
Cd- max out-degree centrality 0.029
Cd max degree centrality 0.518
α powerlaw exponent, degree distribution 1.874
dminα dmin for α 70
α+ powerlaw exponent, in-degree distribution 13.597
dminα+ dmin for α+ 2
σ+ standard deviation, in-degree distribution 47.676
σ- standard deviation, out-degree distribution 5.837
cv+ coefficient variation, in-degree distribution 1,495.23
cv- coefficient variation, out-degree distribution 183.061
σ2+ variance, in-degree distribution 2,273.012
σ2- variance, out-degree distribution 34.07
C+d graph centralization 0.517
z- mean out-degree 7.505
$$deg^{--}(G)$$ max partial out-degree 8
$$\overline{deg^{--}}(G)$$ mean partial out-degree 1.936
$$deg^-_L(G)$$ max labelled out-degree 203
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 3.876
$$deg^-_D(G)$$ max direct out-degree 210
$$\overline{deg^-_D}(G)$$ mean direct out-degree 4.804
z+ mean in-degree 3.385
$$deg^{++}(G)$$ max partial in-degree 3,708
$$\overline{deg^{++}}(G)$$ mean partial in-degree 3.115
$$deg^+_L(G)$$ max labelled in-degree 5
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.087
$$deg^+_D(G)$$ max direct in-degree 1,854
$$\overline{deg^+_D}(G)$$ mean direct in-degree 2.167
$$deg_P(G)$$ max predicate degree 6,178
$$\overline{deg_P}(G)$$ mean predicate degree 98.831
$$deg^+_P(G)$$ max predicate in-degree 3,042
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 51.048
$$deg^-_P(G)$$ max predicate out-degree 1,842
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 31.727
$$\propto_{s-o}(G)$$ subject-object ratio 0.367
$$r_L(G)$$ ratio of repreated predicate lists 0.993
$$deg_{PL}(G)$$ max predicate list degree 1,854
$$\overline{deg_{PL}}(G)$$ mean predicate list degree 152.1
$$C_G$$ distinct classes 12
$$S^C_G$$ all different typed subjects 3,042
$$r_T(G)$$ 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