Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the represented problem. To address cutting-edge problems based on graph data, the research field of Graph Neural Networks (GNNs) has emerged. Despite the field’s youth and the speed at which new models are developed, many recent surveys have been published to keep track of them. Nevertheless, it has not yet been gathered which GNN can process what kind of graph types. In this survey, we give a detailed overview of already existing GNNs and, unlike previous surveys, categorize them according to their ability to handle different graph types and properties. We consider GNNs operating on static and dynamic graphs of different structural constitutions, with or without node or edge attributes. Moreover, we distinguish between GNN models for discrete-time or continuous-time dynamic graphs and group the models according to their architecture. We find that there are still graph types that are not or only rarely covered by existing GNN models. We point out where models are missing and give potential reasons for their absence.

Since the rise of collaborative tagging systems on the web, the tag recommendation task -- suggesting suitable tags to users of such systems while they add resources to their collection -- has been tackled. However, the (offline) evaluation of tag recommendation algorithms usually suffers from difficulties like the sparseness of the data or the cold start problem for new resources or users. Previous studies therefore often used so-called post-cores (specific subsets of the original datasets) for their experiments. In this paper, we conduct a large-scale experiment in which we analyze different tag recommendation algorithms on different cores of three real-world datasets. We show, that a recommender's performance depends on the particular core and explore correlations between performances on different cores.

Bildeten die Keimzellen des Internet noch kleine und einfach strukturierte Netze, so vergrößerten sich sowohl seine physikalischen als auch seine logischen Topologien später rasant. Wuchs einerseits das Netz aus Rechnern als Knoten und Verbindungsleitungen als Kanten immer weiter, so bedienten sich andererseits gleichzeitig immer mehr Anwendungen dieser Infrastruktur, um darüber ihrerseits immer größere und komplexere virtuelle Netze zu weben, z. B. das WWW oder soziale Online-Netze. Auf jeder Ebene dieser Hierarchie lassen sich die jeweiligen Netztopologien mithilfe von Graphen beschreiben und so mathematisch untersuchen. So ergeben sich interessante Einblicke in die Struktureigenschaften unterschiedlicher Graphentypen, die großen Einfluss auf die Leistungsfähigkeit des Internet haben. Hierzu werden charakteristische Eigenschaften und entsprechende Kenngrößen verschiedener Graphentypen betrachtet wie der Knotengrad, die Durchschnittsdistanz, die Variation der Kantendichte in unterschiedlichen Netzteilen und die topologische Robustheit als Widerstandsfähigkeit gegenüber Ausfällen und Angriffen. Es wird dabei Bezug genommen auf analytische, simulative und zahlreiche empirische Untersuchungen des Internets und hingewiesen auf Simulationsprogramme sowie Abbildungen von Internetgraphen im Internet.

The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain.

The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain.

The information contained in social tagging systems is often modelled as a graph of connections between users, items and tags. Recommendation algorithms such as FolkRank, have the potential to leverage complex relationships in the data, corresponding to multiple hops in the graph. We present an in-depth analysis and evaluation of graph models for social tagging data and propose novel adaptations and extensions of FolkRank to improve tag recommendations. We highlight implicit assumptions made by the widely used folksonomy model, and propose an alternative and more accurate graph-representation of the data. Our extensions of FolkRank address the new item problem by incorporating content data into the algorithm, and significantly improve prediction results on unpruned datasets. Our adaptations address issues in the iterative weight spreading calculation that potentially hinder FolkRank's ability to leverage the deep graph as an information source. Moreover, we evaluate the benefit of considering each deeper level of the graph, and present important insights regarding the characteristics of social tagging data in general. Our results suggest that the base assumption made by conventional weight propagation methods, that closeness in the graph always implies a positive relationship, does not hold for the social tagging domain.

The richness of the (Semantic) Web lies in its ability to link related resources as well as data across the Web. However, while relations within particular datasets are often well defined, links between disparate datasets and corpora of Web resources are rare. The increasingly widespread use of cross-domain reference datasets, such as Freebase and DBpedia for annotating and enriching datasets as well as document corpora, opens up opportunities to exploit their inherent semantics to uncover semantic relationships between disparate resources. In this paper, we present an approach to uncover relationships between disparate entities by analyzing the graphs of used reference datasets. We adapt a relationship assessment methodology from social network theory to measure the connectivity between entities in reference datasets and exploit these measures to identify correlated Web resources. Finally, we present an evaluation of our approach using the publicly available datasets Bibsonomy and USAToday.

The richness of the (Semantic) Web lies in its ability to link related resources as well as data across the Web. However, while relations within particular datasets are often well defined, links between disparate datasets and corpora of Web resources are rare. The increasingly widespread use of cross-domain reference datasets, such as Freebase and DBpedia for annotating and enriching datasets as well as document corpora, opens up opportunities to exploit their inherent semantics to uncover semantic relationships between disparate resources. In this paper, we present an approach to uncover relationships between disparate entities by analyzing the graphs of used reference datasets. We adapt a relationship assessment methodology from social network theory to measure the connectivity between entities in reference datasets and exploit these measures to identify correlated Web resources. Finally, we present an evaluation of our approach using the publicly available datasets Bibsonomy and USAToday.

The structure of a large network (graph) can often be revealed by partitioning it into smaller and possibly more dense sub-networks that are easier to handle. One of such decompositions is based on “ k -cores”, proposed in 1983 by Seidman. Together with connectivity components, cores are one among few concepts that provide efficient decompositions of large graphs and networks. In this paper we propose an efficient algorithm for determining the cores decomposition of a given network with complexity $$O(m)$$, where m is the number of lines (edges or arcs). In the second part of the paper the classical concept of k -core is generalized in a way that uses a vertex property function instead of degree of a vertex. For local monotone vertex property functions the corresponding generalized cores can be determined in $$O(motn))$$ time, where n is the number of vertices and Δ is the maximum degree. Finally the proposed algorithms are illustrated by the analysis of a collaboration network in the field of computational geometry.

We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the "six degrees of separation" phenomenon on a global scale. Second, by studying the average local clustering coefficient and degeneracy of graph neighborhoods, we show that while the Facebook graph as a whole is clearly sparse, the graph neighborhoods of users contain surprisingly dense structure. Third, we characterize the assortativity patterns present in the graph by studying the basic demographic and network properties of users. We observe clear degree assortativity and characterize the extent to which "your friends have more friends than you". Furthermore, we observe a strong effect of age on friendship preferences as well as a globally modular community structure driven by nationality, but we do not find any strong gender homophily. We compare our results with those from smaller social networks and find mostly, but not entirely, agreement on common structural network characteristics.

The modeling of realistic networks is of great importance for modern complex systems research. Previous procedures typically model the natural growth of networks by means of iteratively adding nodes, geometric positioning information, a definition of link connectivity based on the preference for nearest neighbors or already highly connected nodes, or combine several of these approaches. Our novel model is based on the well-know concept of k-cores, originally introduced in social network analysis. Recent studies exposed the significant k-core structure of several real world systems, e.g. the AS network of the Internet. We present a simple and efficient method for generating networks which strictly adhere to the characteristics of a given k-core structure, called core fingerprint. We show-case our algorithm in a comparative evaluation with two well-known AS network generators.

In this paper, we discuss two graphs in Wikipedia (i) the article graph, and (ii) the category graph. We perform a graph-theoretic analysis of the category graph, and show that it is a scale-free, small world graph like other well-known lexical semantic networks. We substantiate our findings by transferring semantic relatedness algorithms defined on WordNet to the Wikipedia category graph. To assess the usefulness of the category graph as an NLP resource, we analyze its coverage and the performance of the transferred semantic relatedness algorithms.

The structure of large networks can be revealed by partitioning them to smaller parts, which are easier to handle. One of such decompositions is based on $k$--cores, proposed in 1983 by Seidman. In the paper an efficient, $O(m)$, $m$ is the number of lines, algorithm for determining the cores decomposition of a given network is presented.

The structure of large graphs can be revealed by partitioning graphs to smaller parts, which are easier to handle. In the paper we propose the use of core decomposition as an efficient approach for partitioning large graphs. On the selected subgraphs, computationally more intensive, clustering and blockmodeling can be used to analyze their internal structure. The approach is illustrated by an analysis of Snyder & Kick’s world trade graph.

Social network researchers have long sought measures of network cohesion, Density has often been used for this purpose, despite its generally admitted deficiencies. An approach to network cohesion is proposed that is based on minimum degree and which produces a sequence of subgraphs of gradually increasing cohesion. The approach also associates with any network measures of local density which promise to be useful both in characterizing network structures and in comparing networks.