RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 31,892,842
n graph size (no. of vertices) 2,634,934
dmax max degree 2,046,207
d+max max in-degree 1,822,497
d-max max out-degree 1,442,406
z mean total degree 24.208
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+.
767
h h-index, respecting total degree 981
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.
20,104,090
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.
11,788,752
y reciprocity 0.102
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.
8
PR max pagerank value 0.041
Cd+ max in-degree centrality 0.692
Cd- max out-degree centrality 0.547
Cd max degree centrality 0.777
α powerlaw exponent, degree distribution 1.8
dminα dmin for α 963
α+ powerlaw exponent, in-degree distribution 1.636
dminα+ dmin for α+ 779
σ+ standard deviation, in-degree distribution 2,096.957
σ- standard deviation, out-degree distribution 940.191
cv+ coefficient variation, in-degree distribution 17,324.7
cv- coefficient variation, out-degree distribution 7,767.71
σ2+ variance, in-degree distribution 4,397,230.036
σ2- variance, out-degree distribution 883,959.865
C+d graph centralization 0.777
z-
Effective measure!Score: 0.052

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

mean out-degree 14.158
$$deg^{--}(G)$$ max partial out-degree 865,400
$$\overline{deg^{--}}(G)$$ mean partial out-degree 4.71
$$deg^-_L(G)$$
Effective measure!Score: 0.055

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

max labelled out-degree 86
$$\overline{deg^-_L}(G)$$ mean labelled out-degree 3.006
$$deg^-_D(G)$$
Effective measure!Score: 0.063

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

max direct out-degree 27,400
$$\overline{deg^-_D}(G)$$ mean direct out-degree 5.233
z+ mean in-degree 12.659
$$deg^{++}(G)$$ max partial in-degree 1,822,497
$$\overline{deg^{++}}(G)$$ mean partial in-degree 10.671
$$deg^+_L(G)$$ max labelled in-degree 195
$$\overline{deg^+_L}(G)$$ mean labelled in-degree 1.186
$$deg^+_D(G)$$ max direct in-degree 1,812,401
$$\overline{deg^+_D}(G)$$ mean direct in-degree 4.679
$$deg_P(G)$$ max predicate degree 8,645,823
$$\overline{deg_P}(G)$$ mean predicate degree 53,243.476
$$deg^+_P(G)$$ max predicate in-degree 2,127,912
$$\overline{deg^+_P}(G)$$ mean predicate in-degree 11,303.566
$$deg^-_P(G)$$ max predicate out-degree 605,465
$$\overline{deg^-_P}(G)$$ mean predicate out-degree 4,989.703
$$\propto_{s-o}(G)$$ subject-object ratio 0.811
$$r_L(G)$$ 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 1,612,733
$$\overline{deg_{PL}}(G)$$
Effective measure!Score: 0.231

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

mean predicate list degree 330.358
$$C_G$$
Effective measure!Score: 0.048

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

distinct classes 289
$$S^C_G$$ all different typed subjects 2,127,912
$$r_T(G)$$ ratio of typed subjects 0.948

Plots

Degree distribution shown here
In-degree distribution shown here
Last update of this page: 25 March 2020 13:38:39 CET