Characterizing Complex Network Properties of Knowledge Graphs
Anderson Rossanez
1 a
, Ricardo da Silva Torres
2,3 b
and Julio Cesar dos Reis
1 c
1
Institute of Computing, University of Campinas, Campinas, SP, Brazil
2
Agricultural Biosystems Engineering and Wageningen Data Competence Center, Wageningen University & Research,
Wageningen, The Netherlands
3
Department of ICT and Natural Sciences, Norwegian University of Science and Technology,
˚
Alesund, Norway
Keywords:
Knowledge Graphs, Complex Networks, Centrality Measurements.
Abstract:
Knowledge Graphs have been established as one the most relevant representations to encode knowledge, with
relevant applications in the public and private sectors. One common research direction concerning the analysis
of created knowledge graphs relies on the assumption that their intrinsic properties and structure are similar
to what is observed in complex networks. However, studies concerning identifying typical complex network
structures in knowledge graphs are lacking in the literature. This paper bridges this gap by analyzing com-
monly and recently used knowledge graphs in the semantic web field, seeking to demonstrate their complex
network properties. Evaluation involving DBpedia and Wikidata data confirms the occurrence of intrinsic
complex network structures in their respective knowledge graphs.
1 INTRODUCTION
Knowledge Graphs (KGs) (Ehrlinger and W
¨
oß,
2016) are computational tools that model knowledge
through the interrelations of real-world entities in
facts using a graph structure. Many large-scale KGs
are made freely available, such as DBpedia (Auer
et al., 2007) and Wikidata (Erxleben et al., 2014),
while others are maintained by companies (Noy et al.,
2019), such as Google,
1
for instance. The importance
of KGs as a means of knowledge representation has
been increasing both in academia and industry. Such
importance is proven by the ever-growing amount of
applications that take advantage of them in several do-
mains (Zou, 2020; Ji et al., 2022).
Due to their graph-based representation, several
studies have considered the computation of com-
plex network measurements as a key methodological
procedure in different analysis tasks involving KGs
(D
¨
orpinghaus et al., 2022). More specifically, stud-
ies concerning the use of centrality measurements
computed over KGs have been conducted to deter-
a
https://orcid.org/0000-0001-7103-4281
b
https://orcid.org/0000-0001-9772-263X
c
https://orcid.org/0000-0002-9545-2098
1
https://blog.google/products/search/
introducing-knowledge-graph-things-not/ (As of Aug.
2023).
mine the relevance of concepts represented by their
nodes (Park et al., 2019) or verify how such relevance
changes over time (Rossanez et al., 2020). Other
examples involve determining features over KGs to
support their embedding for machine learning usage
(Sadeghi et al., 2021), such as, for instance, in predic-
tive models (Tilly and Livan, 2021).
Real-life complex networks, represented by large
graphs, present characteristics that distinguish them
from random graphs. Several models of complex
networks are available, and sets of observable char-
acteristics describe them. No studies in the litera-
ture compare the characteristics of complex networks
with those from KGs, which would be valuable to en-
sure the validity of methodologies such as those that
employ complex network measurements in KG-based
analyses.
In this study, we take a step forward to bridge this
gap. Our objective is to demonstrate that KGs present
characteristics of real-life complex network models.
By observing such characteristics, we can safely use
complex network measurements on KG-based anal-
yses. This article assesses complex network proper-
ties based on widely known real-world KGs. To the
best of our knowledge, no studies in the literature per-
formed such an evaluation.
This article addresses the following research ques-
tions:
Rossanez, A., Torres, R. and Reis, J.
Characterizing Complex Network Properties of Knowledge Graphs.
DOI: 10.5220/0012257300003598
In Proceedings of the 15th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2023) - Volume 2: KEOD, pages 119-128
ISBN: 978-989-758-671-2; ISSN: 2184-3228
Copyright © 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
119

RQ1. How can we assess complex network charac-
teristics on KGs?
RQ2. Would widely used KGs present complex net-
work characteristics?
RQ3. Is it sound to apply complex network measure-
ments on KGs?
In this study, we consider two complex network
models, namely scale-free and small-world networks.
We consider the characteristics of such networks in
the scope of the formal definition of KGs, and their
intrinsic properties. We conduct an experimental pro-
cedure involving real-world KGs, namely DBpedia
and Wikidata. We observed the characteristics of our
targeted complex network models in sub-KGs repre-
senting entries of such datasets previously used in the
literature for centrality measurement extraction. We
also observed the same characteristics on instances
of a Temporal Knowledge Graph (TKG) to verify if
they are also observable over time. The results show
the availability of complex network characteristics on
KGs.
In short, the contributions of this investigation are
twofold:
• We found, for the first time, complex network
properties in knowledge graphs;
• We present and discuss an analysis showing that
complex network characteristics are observed in
widely used KGs, which validate ongoing initia-
tives concerning using complex network measure-
ments for KG-based analyses.
The remainder of this article is organized as fol-
lows: Section 2 introduces underlying concepts in this
study. Section 3 presents the related work. Our pro-
posal to observe complex network characteristics in
KGs is detailed in section 4. Section 5 describes our
experimental evaluation and presents the achieved re-
sults, which are discussed in Section 6. Section 7
summarizes our findings and points out directions for
future research.
2 BACKGROUND
We provide an overview of concepts that are relevant
to our formulations: Knowledge Graphs (cf. Subsec-
tion 2.1) and Complex Networks (cf. Subsection 2.2).
2.1 Knowledge Graphs
Knowledge Graphs (KGs) are computational tools ap-
plied to represent knowledge regarding entities and
their relationships (Paulheim, 2017). KGs have re-
cently been exploited by both the industry and the
academia in scenarios that require the representation
of large-scale, diverse, and dynamic collections of
data (Hogan et al., 2021).
A KG defines the interrelations of entities
in facts using (subject, predicate, object) triples.
Most KGs use the Resource Description Framework
(RDF) (Candan et al., 2001) representation. They are
composed of a finite number of RDF triples (Faerber
et al., 2017), in which each of its constituents is repre-
sented by Uniform Resource Identifiers (URIs), liter-
als (which commonly describe the meaning of a URI
in natural language), or even blank nodes. A triple
may be graphically represented by a vertex (predi-
cate) connecting two edges (subject and object) (cf.
Figure 1). The predicate is known as the property of a
triple, whereas the subject and object may be referred
to as entities or concepts.
Figure 1: RDF triple represented as a directed graph in a
visual representation.
KGs may be described in textual files often en-
coded in RDF-based languages, such as Terse RDF
Triple Language
2
, also known as Turtle, or TTL.
In formal terms, a Knowledge Graph K G =
(V ,E) can be represented as a directed graph (di-
graph) containing a set of vertices V and directed
edges E. Vertices represent entities or concepts,
and edges express how such concepts and entities
relate to each other. An RDF triple refers to a
data entity composed of a subject (s), predicate
(p), and an object (o), represented as t = (s, p, o).
In KGs, the edges are, then, a set of predicates,
such that E = {p
0
, p
1
,..., p
n
}. Vertices are, in
turn, a set of subjects and objects, such that V =
{s
0
,s
1
,...,s
n
,o
0
,o
1
,...,o
n
}. A KG may, therefore,
be represented as a set of RDF triples, such that,
K G = {t
0
,t
1
,...,t
n
}, where t
0
= (s
0
, p
0
,o
0
),t
1
=
(s
1
, p
1
,o
1
),...,t
n
= (s
n
, p
n
,o
n
). A predicate p
i
in a
triple t
i
= (s
i
, p
I
,o
i
) is represented as a directed edge
from the subject s
i
to the object o
i
.
2.1.1 Temporal Knowledge Graphs
As knowledge evolves, KGs, likewise, may evolve.
Considering an initial version of a KG, we have a fi-
2
https://www.w3.org/TeamSubmission/turtle/ (As of
Aug. 2023).
KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development
120

nite set of triples. As such KG changes, we may have
at a future time, a different set of triples than we had
in its initial version. As possible changes, new triples
might have been added to the original set. Also, a sub-
set of triples might have been removed from the orig-
inal set. We consider a Temporal Knowledge Graph
(TKG) as a graph that represents not only knowledge
in terms of entities and relationships but also, encodes
how they change over time.
A Temporal Knowledge Graph T K G =
{K G
0
,K G
1
,··· ,K G
m
}, where K G
i
is a KG in
which the triples represent facts that are available in a
determined time frame i, i.e., K G
i
= {t
i
0
,t
i
1
,··· ,t
i
n
}.
In this sense, if we consider KGs in two different time
frames (i and i + 1), i.e., K G
i
= {t
i
0
,t
i
1
,··· ,t
i
n
}, and
K G
i+1
= {t
i+1
0
,t
i+1
1
,··· ,t
i+1
n
}, we may have triples
like t
a
∈ K G
i
and t
a
∈ K G
i+1
, meaning that the fact
described by t
a
is available in both time frames. We
may have triples like t
b
∈ K G
i
and t
b
/∈ K G
i+1
, i.e.,
the fact described by the t
b
is available only in the
time frame i, and not in i + 1.
2.2 Complex Networks
Complex networks can be modeled as large graphs
(Latapy and Magnien, 2008). More specifically (Ro-
drigues, 2019), a complex network can be represented
as a Graph G = (V , E), where V is a set of vertices
V = {v
0
,v
1
,...,v
n
}, representing the nodes of the net-
work, and E = {e
0
,e
1
,...,e
m
} a set of edges, repre-
senting the connections between the nodes of the net-
work, i.e., e
k
= (v
i
,v
j
).
A network can be undirected, i.e., every pair of
edges connecting v
i
to v
j
also connects v
j
to v
i
,
i.e., (v
i
,v
j
) = (v
j
,v
i
). Also, a network can be di-
rected, represented as a digraph (similarly to KGs),
where (v
i
,v
j
) ̸= (v
j
,v
i
). Network edges can also have
weights that indicate the interaction strength between
two nodes. In such cases, they can be represented by
weighted graphs. Since KGs do not weigh their edges,
weighted networks are out of this study’s scope.
Real-world networks often present characteristics
(da F. Costa et al., 2007) that are not observed when
considering random connectivity between the nodes
(Erd
˝
os et al., 1960). Such characteristics are, for in-
stance, (1) community structures (Girvan and New-
man, 2002), i.e., the network nodes can be grouped
into sets, which are internally densely connected; (2)
the “small-world” phenomenon, which refers to the
fact that the average number of edges between nodes
is small, while the clustering coefficient is large, as
described by the small-world network model (Watts
and Strogatz, 1998); and (3) the availability of hubs
and power-law degree distributions, as described by
the scale-free network model (Albert and Barab
´
asi,
2002).
3 RELATED WORK
We searched the literature for studies on complex net-
works and KGs, considering complex network char-
acteristics. In this section, we present a summary of
the studies found adhering to such conditions.
The work by (L
¨
u et al., 2022) reviews studies in-
volving complex networks and KGs. Their work in-
troduced a framework for modeling knowledge based
on complex networks for usage in conjunction with
deep learning models.
The influence of topology on KGs is investigated
in the study by (D
¨
orpinghaus et al., 2022). They eval-
uated the impact of adding extra layers of nodes in
KGs generated following the scale-free and small-
world models. They compared the relevance of nodes
obtained through degree (Freeman, 1978) and be-
tweenness (Brandes, 2001) centralities, before and
after the addition of extra nodes. Also focusing on
topological aspects, the investigation by (Magnanimi
et al., 2023) presented a study concerning the effec-
tiveness of updating portions of KGs. They compared
the results obtained considering distinct properties of
KGs, including their topology. They considered large
KGs following the scale-free, small-world, and even
random KGs.
(Chen et al., 2022) combined KGs and other in-
puts to construct what they call “tripartite” graphs,
used for their recommendation method. They ob-
served such tripartite graphs present properties of
scale-free networks. They benefit from properties,
such as hubs, when embedding their graphs, hence,
improving their recommendation method.
The work by Mantle (Mantle et al., 2019), in turn,
explored the reasoning over large-scale databases, in
special KGs. Although not the focus of their study,
they observed in their evaluation the tendency of KGs
presenting a scale-free topology, typified by a small
number of hubs connected to many nodes, and a large
number of nodes with few connections.
Different from the studies found in the literature,
our present investigation emphasizes specifically ob-
serving complex network properties in widely known
real-world KGs. We seek for characteristics that are
observed in models that describe real-world complex
networks. Our ultimate objective with our experimen-
tal procedure is to assess the use of complex network
measurements (most notably, centrality metrics) on
KGs. To the best of our knowledge, no study in the
literature has performed such an analysis.
Characterizing Complex Network Properties of Knowledge Graphs
121

4 METHOD
We considered two real-world complex network mod-
els and their characteristics. Considering their defini-
tion, we aim to observe whether such characteristics
can be found in KGs. Figure 2 illustrates the observed
characteristics and their best-fitting models. In Sec-
tion 4.1 and Section 4.2, we show how a KG can sat-
isfy the properties of such two specific complex net-
work models.
4.1 Scale-Free Model
Scale-free networks present a degree distribution
asymptotically following a power-law. Such a law
denotes that most nodes in the network have a low
amount of links, while a few important nodes hold
a higher amount of network links. Those are, there-
fore, the main characteristics of the scale-free model,
i.e., degree distribution following power-law, and the
presence of hubs.
At this stage, we describe how we observe such
scale-free model characteristics on KGs, as scale-free
digraphs (Bollobas et al., 2003).
4.1.1 Degree Distribution
Degree distributions relate the degrees (k) of the
nodes in a network with the frequencies (p
k
) in which
they are observed, i.e., p
k
∼ k
−y
(where y is the de-
gree exponent). The degree distribution of scale-free
networks follows a power-law distribution, in which
we observe a high frequency of low-degree nodes and
a low frequency of high-degree nodes. This can be
observed when plotting the distribution in a log-log
scale, in which the data points can be roughly approx-
imated to a straight line, i.e., log p
k
∼ −ylog k, where
log p
k
is expected to be linearly dependent on log k
(Barab
´
asi and P
´
osfai, 2016).
KGs are digraphs; each node has both an in-
degree (k
in
) and an out-degree (k
out
), i.e., the num-
ber of edges pointing towards and away from them,
respectively. This way, the degree of a KG node is
k = k
in
+ k
out
. When adding a directed edge from
node i to node j in a KG, we expect to increase k
i
out
and k
j
in
. In this sense, we can distinguish two distribu-
tions for KGs: in-degree and out-degree distributions,
where, similarly, we expect log p
k
in
∼ −y log k
in
and
log p
k
out
∼ −ylog k
out
4.1.2 Hubs
In networks with power-law degree distribution, most
nodes present only a few links, while a few other
nodes concentrate the majority of links in the net-
work. Such few nodes, called hubs, hold the network
together by linking most less-linked nodes.
Given the digraph nature of KGs, where incoming
and outgoing edges are available, we can distinguish
highly-linked nodes as hubs and authorities (Klein-
berg, 1999). In this domain, hubs are nodes with more
outgoing links, while authorities are those with more
incoming links. We may observe hubs at the tail of
the in-degree distribution, as such region denotes the
few available nodes with the higher in-degree values.
On the other hand, authorities can be analogously ob-
served at the tail portion of out-degree distributions.
4.2 Small-World Model
In small-world networks, despite not being direct
neighbors, most nodes can reach the majority of other
nodes through a small number of steps (i.e., a small
path exists between such nodes). On such networks,
the degree distribution follows Poisson’s distribution.
They display a short average path length and a high
average clustering coefficient. We describe how we
observe such small-world model characteristics on
KGs.
4.2.1 Degree Distribution and Hubs
On small-world networks, the degree distribution fol-
lows Poisson’s distribution. For this reason, we ob-
serve that most of the nodes have an average degree.
This also denotes an overabundance of hubs.
For KGs, we distinguish the degree distribution in
two distinct distributions (cf. Section 4.1.1). There-
fore, we may observe the patterns on p
k
in
vs k
in
and
p
k
out
vs k
out
plots (including the overabundance of
hubs).
4.2.2 Average Short Path Length
Small-world networks present a small average short
path length, denoting the connectivity between most
nodes and that a small path exists between two dis-
tinct nodes in the network. Considering a network
of N nodes, the average short path length (< d >)
is given by < d >=
1
N(N−1)
∑
N
i̸= j
d(i, j), where d(i, j)
is the shortest path length between nodes i and j. If
the network contains disconnected components, then
< d > cannot be calculated due to distances between
some nodes diverging to infinity.
In KGs, the path must consider the direction of
the edges. In this sense, we could have paths in which
we may reach node j from node i. However, we may
not reach node j from node i, i.e., d(i, j) ̸= d( j.i).
KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development
122

Figure 2: Complex Network properties’ assessment. We observe such characteristics on KGs to verify the best-fitting
model.
Furthermore, the KG must be strongly connected to
calculate the average shortest path length.
4.2.3 Average Clustering Coefficient
Small-world networks present a high average cluster-
ing coefficient. The clustering coefficient (C
i
) of a
node i denotes how linked to each other its neigh-
bors are. The value ranges from 0 to 1, represent-
ing no connectivity and full connectivity, respectively.
The average value (< C)) computes the metric for all
the nodes in the network. It is defined as < C >=
1
N
∑
N
i=1
C
i
.
For KGs and their possibility of incoming and out-
going edges between the nodes, to consider complete
connectivity, there should be at least one incoming
and an outgoing edge between a node’s neighbors.
5 EVALUATION
We performed an analysis to assess if widely used
KGs present characteristics that are observed in real-
world complex networks rather than random net-
works. We considered the characteristics of two mod-
els of complex networks: Scale-free and Small-world
(cf. Section 4). We computed from the KGs, their de-
gree distributions, and the availability of hubs. Also,
we sought to compute their average short path lengths
and average clustering coefficients.
We conducted such evaluation
3
on subgraphs of
3
https://github.com/rossanez/complexnw-kg (As of
Aug. 2023).
two well-known widely-used KGs: DBpedia (cf. Sec-
tion 5.1) and Wikidata (cf. Section 5.2). We took
two portions of such knowledge bases (i.e., sub-KGs),
from which centrality measurements were extracted
from studies found in the literature, aiming for dis-
tinct objectives. In one study (Kalloubi et al., 2016), a
sub-KG comprising all the relationships about the Or-
acle corporation entity, from DBpedia was used. In
another one (Puspa Rinjeni et al., 2022), relationships
from the Movie entity, from both DBpedia
45
and Wiki-
data
67
were used. In our procedure, we first observed
the characteristics of each of the sub-KGs alone, and
then we merged both into a single KG, to confirm if
the same characteristics were still observed. The first
and second sub-KGs represent the relationships of the
same chosen entities on both knowledge bases. Fig-
ure 3 illustrates the adopted procedure.
Finally, we considered observing the same charac-
teristics on a TKG (cf. Section 5.3), to verify if such
real-world complex networks’ characteristics can also
change over time. The TKG used in this analysis was
generated in a recent study (Rossanez et al., 2020)
for centrality measurement extraction. In the follow-
ing, we present the observed characteristics in all the
aforementioned KGs.
4
https://dbpedia.org/data/Oracle
Corporation.ttl (As of
Aug. 2023).
5
https://dbpedia.org/data/Movie.ttl (As of Aug. 2023).
6
https://www.wikidata.org/wiki/Special:EntityData/
Q19900.ttl (As of Aug. 2023).
7
https://www.wikidata.org/wiki/Special:EntityData/
Q11424.ttl (As of Aug. 2023).
Characterizing Complex Network Properties of Knowledge Graphs
123

Figure 3: KG creation procedure. Applied to DBpedia and Wikidata. We took two portions of each database (i.e., the 1st
and 2nd sub-KGs), corresponding to all the relationships about the Oracle corporation, and Movie entities, respectively.
Figure 4: DBpedia in-degree distributions. All sub-KGs
present a power-law pattern.
5.1 Results on the DBpedia Analysis
Figure 4 shows the in-degree distributions for the
three sub-KGs retrieved from DBpedia.
We observe that all cases follow a similar distribu-
tion, where most nodes present a low in-degree, while
few concentrate higher degrees. The behavior resem-
bles a power-law distribution. Figure 5 shows the out-
degree distributions for the same sub-KGs, and we
observe similar patterns.
Another aspect evidenced by a few higher-in-
degree nodes is that, although not over-abundant, we
found the presence of hubs, as observed in the tail
portion of the distribution illustrated by Figure 4.
Table 1 presents computed metrics obtained for
Figure 5: DBpedia out-degree distributions. All sub-KGs
present a power-law pattern.
the KGs under analysis. We observe in all cases that
the density of the KGs is very small. Considering the
number of available nodes, the number of observed
edges is too small when compared to the number of
directed edges that would be necessary for a complete
digraph (i.e., two edges – one in each direction – for
each pair of available edges).
In addition, such graphs are not strongly con-
nected. For this reason, it is not possible to calcu-
late the average short path length. As those directed
graphs are sparse, reaching all nodes starting from a
randomly given node is impossible. A small average
short path length would be necessary in the small-
world network model. Another condition for such a
model would be a high average clustering coefficient.
KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development
124

Table 1: Metrics for DBpedia KGs. Number of nodes (N),
edges (E), density (D), average short path length (< d >),
and average clustering coefficient (< C >).
N E D < d > < C >
Oracle 2143 2577 0.00056 N/A 0.0
Movie 3411 3460 0.00029 N/A 0.0
Merged 5554 6037 0.00019 N/A 0.0
Figure 6: Wikidata in-degree distribution. All sub-KGs
present a power-law pattern.
Table 1 presents the KGs have practically zero cluster-
ing coefficient, also explained by the very low number
of edges for the available nodes.
Such KGs, therefore, better fit the scale-free net-
work model due to the observed power-law degree
distribution and presence of hubs, rather than the
small-world model, as they do not have a small aver-
age short path length and small clustering coefficient.
The KGs are not random and display characteristics
of real-life complex networks.
5.2 Results on the Wikidata Analysis
Figure 6 presents the degree distributions for the three
sub-KGs retrieved from Wikidata.
Similarly to what we observed from the results re-
garding DBpedia analysis, all three KGs’ degree dis-
tributions resemble a power-law distribution. We in-
dicate the presence of hubs at the tail of the in-degree
distribution. Figure 7 shows the out-degree distribu-
tions for the same sub-KGs, and we observe similar
patterns.
Table 2 presents the metrics obtained for the Wiki-
data KGs. The density of the KGs, although still
small, is slightly higher when compared to DBpe-
dia. We found a higher amount of edges for the given
nodes available (i.e., Wikidata KGs have more triples
than those of DBpedia).
Figure 7: Wikidata out-degree distribution. All sub-KGs
present a power-law pattern.
Table 2: Metrics for Wikidata KGs. Number of nodes (N),
edges (E), density (D), average short path length (< d >),
and average clustering coefficient (< C >).
N E D < d > < C >
Oracle 3052 7275 0.00078 N/A 0.00806
Movie 4069 8741 0.00052 N/A 0.00721
Merged 6530 15051 0.00035 N/A 0.00692
The KGs are similarly not strongly connected,
so their average shortest path lengths cannot be de-
termined. They present a higher clustering coeffi-
cient than DBpedia’s, although still very small (the
value ranges from 0 to 1). The higher amount of
triples/edges available can also explain the increase.
Similar to DBpedia, such KGs are a better fit for
the scale-free network model rather than the small-
world model. We can, therefore, also indicate these
KGs are not random and display properties of real-
world complex networks.
5.3 Results on the Temporal KG
Analysis
We considered three temporal instances of a TKG
generating from abstracts of an annual scientific
event, more specifically, representing the editions of
2019, 2020, and 2021 of the International Semantic
Web Conference
8
(ISWC). Figure 8 presents the in-
degree distributions of the three referred temporal in-
stances.
Similar to the other observed cases, they follow
a power-law distribution pattern, evidencing the pres-
ence of hubs. Figure 9 shows the out-degree distribu-
tions for the same sub-KGs. Table 3 shows that the
8
https://link.springer.com/conference/semweb (As of
Aug. 2023).
Characterizing Complex Network Properties of Knowledge Graphs
125

Figure 8: TKG in-degree distribution. All three instances
present a power-law pattern.
Figure 9: TKG out-degree distribution. All three in-
stances present a power-law pattern.
Table 3: Metrics for TKG. Number of nodes (N), edges
(E), density (D), average short path length (< d >), and av-
erage clustering coefficient (< C >).
N E D < d > < C >
2019 12285 24984 0.00016 N/A 0.02860
2020 10618 21147 0.00018 N/A 0.02932
2021 8003 15672 0.00024 N/A 0.02923
temporal instances present a small density. However,
it shows larger edges (triples) for the available nodes.
Like the other cases, neither of the temporal in-
stances is strongly connected, so the average short
path length cannot be calculated. They also present
a small average clustering coefficient. Following the
same outcome of the previously analyzed KGs, the
temporal instances of the TKG fit the scale-free net-
work model and not the small-world model. In addi-
tion, we found that the characteristics are maintained
over time, allowing us to state that the TKG is not ran-
dom and displays characteristics of real-world com-
plex networks. It is worth mentioning that no sub-
stantial changes in complex network patterns were
observed in the temporal evolution.
6 DISCUSSION
The results presented in Section 5 indicated that
real-world KGs present characteristics of complex
network models in KGs. While, in theory, com-
plex networks may be represented by random graphs
(Erd
˝
os et al., 1960), models describe real-world com-
plex networks (Watts and Strogatz, 1998; Albert and
Barab
´
asi, 2002) presenting characteristics that are not
observed when considering random behavior. Most
notably, some of such characteristics are power-law
degree distribution, presence of hubs, high clustering
coefficient, etc.
To observe such characteristics in KGs, we had
to refer to their definition, considering a digraph that
allows multiple parallel edges. To address our first re-
search question (i.e., RQ1), we then had to transpose
the expected properties from non-directed graphs that
represent complex networks to the KG domain. Our
results on real-world KGs indicate their tendency to
follow the scale-free model, in which the degree dis-
tributions, more specifically of both in-degree and
out-degrees, follow a power-law. This means that on
real-world KGs, we are expected to encounter few
nodes with higher degree nodes, and many nodes
with low degree. This, in turn, indicates the presence
of not-over-abundant hubs, represented by the fewer
nodes with the highest degrees.
While presenting a good fit for scale-free models,
real-life KGs did not present the characteristics ex-
pected for the small-world model. We observed that
real-life KGs have low density, i.e., and have a small
number of edges, in comparison with their number of
nodes. Furthermore, real-life KGs often present dis-
joint portions, making them not strongly connected.
Considering such aspects, we expect a low average
clustering coefficient and a high average short path
length. Despite not fitting such a model, we did ob-
serve a tendency in all evaluated KGs to follow the
scale-free model. For this reason, we can positively
answer RQ2.
We chose to include a TKG in our study, as cen-
trality measurements are employed to characterize
the knowledge evolution over TKGs in the literature
(Rossanez et al., 2020). The analyzed TKG presented
the same characteristics in all the temporal instances.
The power-law degree distribution and presence of
hubs were consistently observed, as well as a small
KEOD 2023 - 15th International Conference on Knowledge Engineering and Ontology Development
126

clustering coefficient and not-strongly connectedness.
All instances, therefore, have shown a good fit for the
scale-free model.
Of course, the KGs observed in this study do not
correspond to the totality of the datasets they were
obtained from. Despite our efforts to observe dis-
tinct portions of them, which hindered the same re-
sults, there is a possibility that a random portion not
covered by this study might fail to present the same
results. We could have considered more large-scale
KGs besides DBpedia and Wikidata, to further assure
our findings. Other complex network characteristics,
such as, for instance, the availability of communities
(Girvan and Newman, 2002), can be explored, as well
as other models that describe such networks (Ander-
son and Dragi
´
cevi
´
c, 2020). On the other hand, the
obtained results suggest that, indeed, KGs hold rele-
vant properties of complex networks.
With such a statement, we, thus, positively answer
our final research question (i.e., RQ3). Complex net-
works measurements, especially centrality metrics,
can, therefore, be used with confidence in KG-based
analysis, as already being done in several research
studies (D
¨
orpinghaus et al., 2022; Park et al., 2019;
Rossanez et al., 2020; Sadeghi et al., 2021; Tilly and
Livan, 2021).
7 CONCLUSION
This study investigated the complex network proper-
ties found in well-known and recently used knowl-
edge graphs. To the best of our knowledge, this is
the first study focusing on demonstrating those prop-
erties. Performed evaluations involving the DBpedia
and the Wikidata knowledge graphs to confirm their
complex network properties, therefore validating ex-
isting studies dedicated to the use of complex net-
work measurements in the characterization of knowl-
edge graphs (e.g., relevance of concepts) (Rossanez
et al., 2020). Future work encompasses the analysis of
the temporal evolution of complex network properties
found in relevant knowledge graphs and the connec-
tion of those properties with the effectiveness of typ-
ical reasoning algorithms. We plan to investigate the
creation of synthetic knowledge graphs and their use
for training machine learning algorithms. The cre-
ation of those synthetic datasets would comply with
pre-defined network properties (Dadauto et al., 2023).
ACKNOWLEDGEMENTS
This work was supported by the S
˜
ao Paulo Research
Foundation (FAPESP) (Grant #2022/15816-5)
9
.
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