RDF Graph Measures for the Analysis of RDF Graphs

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Measures

Notation Description Value
m graph volume (no. of edges) 3,244,898
n graph size (no. of vertices) 809,832
dmax max degree 262,348
d+max max in-degree 262,348
d-max max out-degree 235
z mean total degree 8.014
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+.
342
h h-index, respecting total degree 352
pmu fill, respecting unique edges only 0
p fill, respecting overall edges 0
mp
Effective measure!Score: 0.045

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.
3,729
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.
3,241,169
y reciprocity 0.003
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 0.004
Cd+ max in-degree centrality 0.324
Cd- max out-degree centrality 0
Cd max degree centrality 0.324
α powerlaw exponent, degree distribution 3.89
dminα dmin for α 16
α+ powerlaw exponent, in-degree distribution 27.017
dminα+ dmin for α+ 1
σ+ standard deviation, in-degree distribution 640.523
σ- standard deviation, out-degree distribution 6.559
cv+ coefficient variation, in-degree distribution 15,985.6
cv-
Effective measure!Score: 0.047

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

coefficient variation, out-degree distribution 163.694
σ2+ variance, in-degree distribution 410,269.698
σ2- variance, out-degree distribution 43.021
C+d graph centralization 0.324
z- mean out-degree 12.344
deg(G) max partial out-degree 210
deg(G) mean partial out-degree 1.277
degL(G)
Effective measure!Score: 0.099

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

max labelled out-degree 16
degL(G) mean labelled out-degree 9.669
degD(G) max direct out-degree 233
degD(G) mean direct out-degree 12.33
z+ mean in-degree 4.01
deg++(G) max partial in-degree 262,348
deg++(G) mean partial in-degree 4.001
degL+(G) max labelled in-degree 3
degL+(G) mean labelled in-degree 1.002
degD+(G) max direct in-degree 262,299
degD+(G)
Effective measure!Score: 0.128

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

mean direct in-degree 4.005
degP(G) max predicate degree 750,378
degP(G) mean predicate degree 95,438.176
degP+(G) max predicate in-degree 262,299
degP+(G) mean predicate in-degree 74,758.529
degP(G) max predicate out-degree 261,722
degP(G) mean predicate out-degree 23,856.088
so(G) subject-object ratio 0.324
rL(G) ratio of repreated predicate lists 0.992
degPL(G)
Effective measure!Score: 0.047

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

max predicate list degree 55,504
degPL(G)
Effective measure!Score: 0.129

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

mean predicate list degree 127.796
CG
Effective measure!Score: 0.06

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

distinct classes 2
SGC all different typed subjects 262,299
rT(G) ratio of typed subjects 0.998

Plots

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