The emergence of Linked Open Data (LOD) enables data on the Web to have a well defined structure and thereby to represent and interlink information from different sources and application areas. This web of data is a complex socially created network, where concepts and relations are connected in intricate ways, collectively forming a network of knowledge. These data are published in a decentralized fashion and they stem from different sources, have different types of relationships, and use different terminologies, ontologies and meta models. While this so-called LOD cloud has become a very valuable resource, we know only very little about the general structural properties of the contained data, which impedes our ability to use and organize this resource in an efficient and accurate manner. The objective of this paper is to provide a basic understanding of LOD from the point of view of network structures. We analyze LOD networks with respect to fundamental network properties such as degree distribution and clustering. Using these metrics, we compare our results to non-LOD networks, such as email, Web, and protein networks, that have been reported in the literature. Our results show that the LOD cloud exhibits a broad variety of different network structures, consistent with the diversity found in other types of networks.
The Linked Open Data (LOD) cloud has grown to huge dimensions in the re‐
cent past, currently consisting of tens of billion triples [
In graph theory terms, it is a directed network of nodes (represented by
URIs and typed string literals), interconnected by labeled, directed edges
(where these labels are URIs too). In a certain sense, each label (i.e. RDF
property) can be seen to represent its own network. The LOD cloud includes
networks about, for example, friend relationships, geographical inclusion, and
relatedness of concepts. The structural properties of these networks are impor‐
tant in many different respects. Scale-free networks, for example, have shown
to be tolerant to random errors, but vulnerable to targeted attacks [
In the study presented here, we want to discover the quantitative properties
of the networks found in the Linked Open Data cloud. We are particularly in‐
terested in how uniform or different they are, whether they all exhibit similar
network structures or whether there is a great variety. Finally, we want to
compare these network properties to "real-world" networks, as they have been
reported in the literature. Do knowledge networks, as we call them, found in
the Linked Open Data cloud have a different structure than other types of
networks that have been investigated so far?
Linked Open Data is one of the largest data sources on the Web, including big
datasets such as DBpedia [14], and it is growing at a fast pace [21,19]. This
data source is by definition distributed and therefore difficult to access and
handle in its entirety. However, the recent development of the LOD Laundro‐
mat platform [
Various studies have been conducted on how the Linked Open Data cloud
can be better explored and interlinked [
Outside of the Linked Open Data domain, many real-world networks have
been analyzed in the past, including router networks, the Web, protein inter‐
action networks, metabolic networks, and emails [
Little is known about the information-theoretic properties of real-world
RDF data. Several structural properties of RDF data are known to follow a
power-law distribution. This includes the size of RDF documents, the fre‐
quency with which terms occur and the frequency with which schema re‐
sources (properties and classes) occur in the data [
To analyze the structure and variety of knowledge networks, we focus our study on the following eight network properties, which cover all important and generally established basic network metrics: the average degree of nodes (i.e. average number of incoming and outgoing edges), the average local clustering coefficient (i.e. average chance of two neighbors of a given node being con‐ nected too), the global clustering coefficient (i.e. ratio of three connected nodes being fully connected), the number of connected components (i.e. sub‐ sets of a network where each node is directly or indirectly linked to every other node in the subset), the α exponent of a power-law fit as an indication of a scale-free network, whether the network is bi-partite or not (i.e. whether the nodes can be divided into two disjoint classes A and B, such that all edges point from A to B and never the other way round), the Gini coefficient of the degree distribution (i.e. the inequality of the degree distribution), and the Gini coefficient of the component size distribution (i.e. the inequality of the compo‐ nent sizes).
To calculate these metrics, we picked a number of widely used RDF proper‐ ties from various vocabularies and domains, attempting to capture the variety of Linked Data (but at this point without claiming representativeness of the sample). We chose foaf:knows as a representative of a property on social rela‐ tions, geop:hasBorderWith as a property of geographical proximity, osspr:con‐ tains/osspr:within as an example of relations about hierarchical inclusions, and swrc:affiliation as a social/organizational network. For comparison and ex‐ ploration, we also included three properties for which we did not expect to find interesting network structures, because their semantics do not seem to de‐ scribe a relation that would form a complex network: lexinfo:partOfSpeech, which maps words to their roles in a sentence, gn:parentCountry, which links geographical entities to the containing countries, and tag:associatedTag, which maps concepts to tag strings. Table 1 shows an overview of these selected properties with their official descriptions.
In addition, we look at a number of properties from the well-known and popular SKOS (Simple Knowledge Organization System) ontology [15]. Specifically, skos:narrower specifies a given concept to be in some sense less general than a given more general concept, whereas skos:related states that two concepts are related without marking one or the other as more general. Similarly, skos:closeMatch, skos:exactMatch, skos:broadMatch, skos:narrow‐ Match, and skos:relatedMatch establish links between concepts, but these so called mapping relations establish links across different concept schemes. For comparison, we also add skos:hasTopConcept, which maps concept schemes to their top concepts, and for which we do not expect to find complex network structures.
On the technical side, we retrieve the instances of these RDF properties from the Linked Open Data cloud by the use of the LOD Laundromat via the Frank tool [19]. We download the triples in N-Quads format, which we trans‐ form then in a straight-forward way using a SWI Prolog program into the Graph Modeling Language (GML) for further processing. We then use the igraph package of R Studio to calculate the different network metrics. Gephi is used with its OpenOrd plugin to visualize the networks.
Standard R commands are used to calculate the metrics, specifically ecount, vcount, degree, transitivity (for clustering coefficients), components (to calcu‐ late weak components), and bipartite_mapping, and ineq (for inequality anal‐ ysis using the Gini coefficient). A power law fit is performed on the degree dis‐ tribution (Kolmogorov-Smirnov test) with the command fit_power_law. A power law exponent α between 2 and 3 is typical for scale-free networks (even though not sufficient to determine their scale-free nature). Below we present the results of our analyses. We explain the sizes of the ana‐ lyzed networks, show visualizations of them, describe them in terms of the in‐ troduced metrics, and finally compare these numbers to results that have been reported in the existing literature.
Network visualizations can be very helpful to get a feeling of the network structures and as an exploratory aid. Figure 1 shows the visualizations of the first part of the analyzed networks. The full foaf:knows network was too large to visualize, which is why we can only show here a visualization of its Last.fm subset. foaf:knows (Last.fm subset) geop:hasBorderWith osspr:contains The variety of appearance of the networks through these visualizations is striking. Social, geographical, and containment relations each exhibit a very particular and clearly distinguishable form. The two relations osspr:contains and its inverse osspr:within, which are semantically identical apart from their direction (which was not taken into account by the visualization algorithm), show similar visual features but are nevertheless clearly different in their structure. lexinfo:partOfSpeech and gn:parentCountry, as expected, do not ex‐ hibit proper network structures, but instead show large and small groups around central objects. These central objects are of course the part of speech categories and countries, respectively. The case of tag:associatedTag, however, gave us a surprising result. We expected this network to be as monotonic as the previous two, but to our surprise it seems to possess a complex network structure. The explanation for this is that seemingly basic relations (from a network point of view), such as a relation between concepts and their informal tags, can lead to complex networks if the relation is many-to-many. Concepts are indirectly linked to related concepts via their overlapping tags, thereby es‐ tablishing a kind of relatedness network, which can exhibit complex struc‐ tures. The RDF properties discussed above stem from different vocabularies, which were defined by different people and are used by different user groups. To find out whether the observed variety is possibly explained by these differences alone, we can look at the different relations from the SKOS vocabulary, which were all defined by the same people and presumably used by the same user groups. Figure 2 shows the visualizations of the chosen SKOS properties. While not quite as varied as the examples shown above, they nevertheless ex‐ hibit a striking variety of network structures. Visualization are good for exploration and for getting an intuitive feeling of the networks, but we now need an objective analysis by quantitative measures. Table 3 shows the results for the chosen network metrics that were introduced above.
The average degree ranges from 1.48 for skos:narrowMatch to above 3.4 for geop:hasBorderWith and osspr:within. As expected, our examples for compari‐ son, lexinfo:partOfSpeech, gn:parentCountry, tag:associatedTag, and skos:hasTopConcept, show a bipartite network structure (i.e. no entities show up on both sides of the relation) or have at least zero or near-zero clustering coefficients. The remaining relations show a relatively broad range of cluster‐ ing behavior up to around 0.65 for osspr:contains and osspr:within on the av‐ erage local clustering coefficient, and up to 0.23 for the global coefficient and geop:hasBorderWith.
Three networks exhibit an α exponent of a power law fit between 2 and 3, which is an indication of a scale-free structure: the Last.fm subset of foaf:knows, swrc:affiliation, skos:related, skos:narrower, and skos:narrowMatch. In addition, the full foaf:knows network, osspr:contains, and tag:associatedTag are outside but very close to the boundary values. Further investigation would be needed, however, to reliably determine whether these networks are indeed scale-free.
The inequality measures in the form of the Gini coefficient on the degree distribution show that this distribution ranges from fairly equal for some of the SKOS predicates to fairly unequal in the case of foaf:knows. An even wider variety is manifested for the inequality with respect to the size of the net‐ work's connected components. From highly unequal (because one giant compo‐ nent includes almost all nodes in the network), such as 0.99 for the Last.fm subset of foaf:knows, to very equal in the case of skos:exactMatch with a value of 0.19.
So far, we have seen a large variety of results for the chosen network metrics
in the LOD cloud, but we do not know so far how this variety compares to
non-LOD networks, which have been studied extensively. For this comparison,
we use nine well-studied networks that have been summarized in the litera‐
ture, including their average degrees and average local clustering coefficient
[
Degree Comparison Linked Data other networks majority of the other networks have a higher average degree than any of the analyzed LOD networks. Only four LOD networks have an average degree that is higher than the lowest of the non-LOD ones. Therefore, while LOD net‐ works show a relatively wide range of average degrees, they do not reach near the top of the scale. This can be explained by the fact that LOD networks are by design incomplete (everybody is free to add more nodes and edges), whereas the other networks stem from data with stronger completeness claims.
Clustering Comparison
We have shown that there is a large variety of network structures in the LOD cloud. Their visualizations show striking differences, and sometimes the struc‐ ture of a given network is hard to anticipate and the results can be surprising, which underscores the importance of our work. While the observed metrics are similar to some other networks reported in the literature, their distributions seem to be slightly different, which might be due to LOD's lack of complete‐ ness.
The study of the degree of completeness and its consequences is in fact one of our future plans. We furthermore plan to conduct studies that take the di‐ rectedness of LOD networks into account, instead of analyzing them only as if they were undirected networks. A further important point to consider in the future are entailed relations. Our two networks for osspr:within and osspr:con‐ tains, for example, entail each other, as they are defined as inverse properties. They therefore form just one network on the semantic level. Similarly, the diff‐ fferent SKOS properties, as many other LOD properties, are arranged in a hi‐ erarchy, and their relation instances can therefore be inferred in well-defined cases, even if the instance has not been explicitly asserted.
It is clear that the analyses shown in this paper have just scratched the sur‐ face, and there is much more to analyze and understand. We hope that our work can provide a basis for such future endeavors.