arXiv subjects
Publications and source records attributed to Jérôme Kunegis.
This is the handbook for the KONECT project, the \emph{Koblenz Network Collection}, a scientific project to collect, analyse, and provide network datasets for researchers in all related fields of research, by the Namur Center for Complex Systems (naXys) at the University of Namur, Belgium, with web hosting provided by the Institute for Web Science and Technologies (WeST) at the University of Koblenz--Landau, Germany.
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of cycles of given lengths. Algorithms for the generation of synthetic graphs are often based on graph growth models, i.e., rules of adding (and sometimes removing) nodes and edges to a graph that mimic the processes present in real-world networks. While such graph generators are desirable from a theoretical point of view, they are often only able to reproduce a narrow set of properties of real-world networks, resulting in graphs with otherwise unrealistic properties. In this article, we instead evaluate common graph generation algorithms at the task of reproducing the numerical statistics of real-world networks, such as the clustering coefficient, the degree assortativity, and the connectivity. We also propose an iterative algorithm, the Guided Graph Generator, based on a greedy-like procedure that recovers realistic values over a large number of commonly used graph statistics, while at the same time allowing an efficient implementation based on incremental updating of only a small number of subgraph counts. We show that the proposed algorithm outperforms previous graph generation algorithms in terms of the error in the reconstructed graphs for a large number of graph statistics such as the clustering coefficient, the assortativity, the mean node distance, and also evaluate the algorithm in terms of precision, speed of convergence and scalability, and compare it to previous graph generators and models. We also show that the proposed algorithm generates graphs with realistic degree distributions, graph spectra, clustering coefficient distributions, and distance distributions.
We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of drawing large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common "hairball" look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model, connectivity and link prediction. We show that in all three cases, a dominant trend towards shrinking diversity is apparent, both theoretically and empirically. In previous work, many kinds of different data have been modeled as networks: social structure, navigational structure, transport infrastructure, communication, etc. Almost all these types of networks are not static structures, but instead dynamic systems that change continuously. Thus, an important question concerns the trends observable in these networks and their interpretation in terms of existing network models. We show in this article that most numerical network characteristics follow statistically significant trends going either up or down, and that these trends can be predicted by considering the notion of diversity. Our work extends previous work observing a shrinking network diameter to measures such as the clustering coefficient, power-law exponent and random walk return probability, and justifies preferential attachment models and link prediction algorithms. We evaluate our hypothesis experimentally using a diverse collection of twenty-seven temporally evolving real-world network datasets.
A detailed understanding of users contributes to the understanding of the Web's evolution, and to the development of Web applications. Although for new Web platforms such a study is especially important, it is often jeopardized by the lack of knowledge about novel phenomena due to the sparsity of data. Akin to human transfer of experiences from one domain to the next, transfer learning as a subfield of machine learning adapts knowledge acquired in one domain to a new domain. We systematically investigate how the concept of transfer learning may be applied to the study of users on newly created (emerging) Web platforms, and propose our transfer learning-based approach, TraNet. We show two use cases where TraNet is applied to tasks involving the identification of user trust and roles on different Web platforms. We compare the performance of TraNet with other approaches and find that our approach can best transfer knowledge on users across platforms in the given tasks.
We analyse the corpus of user relationships of the Slashdot technology news site. The data was collected from the Slashdot Zoo feature where users of the website can tag other users as friends and foes, providing positive and negative endorsements. We adapt social network analysis techniques to the problem of negative edge weights. In particular, we consider signed variants of global network characteristics such as the clustering coefficient, node-level characteristics such as centrality and popularity measures, and link-level characteristics such as distances and similarity measures. We evaluate these measures on the task of identifying unpopular users, as well as on the task of predicting the sign of links and show that the network exhibits multiplicative transitivity which allows algebraic methods based on matrix multiplication to be used. We compare our methods to traditional methods which are only suitable for positively weighted edges.
The political discourse in Western European countries such as Germany has recently seen a resurgence of the topic of refugees, fueled by an influx of refugees from various Middle Eastern and African countries. Even though the topic of refugees evidently plays a large role in online and offline politics of the affected countries, the fact that protests against refugees stem from the right-wight political spectrum has lead to corresponding media to be shared in a decentralized fashion, making an analysis of the underlying social and mediatic networks difficult. In order to contribute to the analysis of these processes, we present a quantitative study of the social media activities of a contemporary nationwide protest movement against local refugee housing in Germany, which organizes itself via dedicated Facebook pages per city. We analyse data from 136 such protest pages in 2015, containing more than 46,000 posts and more than one million interactions by more than 200,000 users. In order to learn about the patterns of communication and interaction among users of far-right social media sites and pages, we investigate the temporal characteristics of the social media activities of this protest movement, as well as the connectedness of the interactions of its participants. We find several activity metrics such as the number of posts issued, discussion volume about crime and housing costs, negative polarity in comments, and user engagement to peak in late 2015, coinciding with chancellor Angela Merkel's much criticized decision of September 2015 to temporarily admit the entry of Syrian refugees to Germany. Furthermore, our evidence suggests a low degree of direct connectedness of participants in this movement, (i.a., indicated by a lack of geographical collaboration patterns), yet we encounter a strong affiliation of the pages' user base with far-right political parties.
In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of triangles. After a review of the concepts of triangle closing and preferential attachment, we present our argument, as well as a simplified model in which preferential attachment can be derived mathematically from triangle closing. Additionally, we perform experiments on synthetic graphs to demonstrate the emergence of preferential attachment in graph growth models based only on triangle closing.
How can we recognise social roles of people, given a completely unlabelled social network? We present a transfer learning approach to network role classification based on feature transformations from each network's local feature distribution to a global feature space. Experiments are carried out on real-world datasets. (See manuscript for the full abstract.)
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by tuning a model parameter $α$. We provide analytic solutions to the quantum walks for the star and circulant graph classes that are valid for an arbitrary value of the number of nodes $N$, time $t$ and the model parameter $α$. We discuss quantitative and qualitative aspects of quantum walks based on directed graphs and their undirected counterparts. Numerical simulations of quantum walks on circulant graphs show complex interference phenomena and how complete suppression of transport is achieved near $α=π/2$. By proving two mirror symmetries around $α=0$ and $π/2$ we show that these quantum walks have a period of $π$ in $α$. We show that undirected edges lose their effect on the quantum walk at $α=π/2$ and present non-bipartite graphs that exhibit suppression of transport. Finally, we analytically compute the Hamiltonians of quantum walks on the directed ring graph.
We perform a large-scale analysis of third-party trackers on the World Wide Web from more than 3.5 billion web pages of the CommonCrawl 2012 corpus. We extract a dataset containing more than 140 million third-party embeddings in over 41 million domains. To the best of our knowledge, this constitutes the largest web tracking dataset collected so far, and exceeds related studies by more than an order of magnitude in the number of domains and web pages analyzed. We perform a large-scale study of online tracking, on three levels: (1) On a global level, we give a precise figure for the extent of tracking, give insights into the structure of the `online tracking sphere' and analyse which trackers are used by how many websites. (2) On a country-specific level, we analyse which trackers are used by websites in different countries, and identify the countries in which websites choose significantly different trackers than in the rest of the world. (3) We answer the question whether the content of websites influences the choice of trackers they use, leveraging more than 90 thousand categorized domains. In particular, we analyse whether highly privacy-critical websites make different choices of trackers than other websites. Based on the performed analyses, we confirm that trackers are widespread (as expected), and that a small number of trackers dominates the web (Google, Facebook and Twitter). In particular, the three tracking domains with the highest PageRank are all owned by Google. The only exception to this pattern are a few countries such as China and Russia. Our results suggest that this dominance is strongly associated with country-specific political factors such as freedom of the press. We also confirm that websites with highly privacy-critical content are less likely to contain trackers (60% vs 90% for other websites), even though the majority of them still do contain trackers.
The mean and variance of the number of appearances of a given subgraph $H$ in an Erdős--Rényi random graph over $n$ nodes are rational polynomials in $n$. We present a piece of software named Polcovar (from "polynomial" and "covariance") that computes the exact rational coefficients of these polynomials in function of $H$.
In this paper, we study the network of global interconnections between language communities, based on shared co-editing interests of Wikipedia editors, and show that although English is discussed as a potential lingua franca of the digital space, its domination disappears in the network of co-editing similarities, and instead local connections come to the forefront. Out of the hypotheses we explored, bilingualism, linguistic similarity of languages, and shared religion provide the best explanations for the similarity of interests between cultural communities. Population attraction and geographical proximity are also significant, but much weaker factors bringing communities together. In addition, we present an approach that allows for extracting significant cultural borders from editing activity of Wikipedia users, and comparing a set of hypotheses about the social mechanisms generating these borders. Our study sheds light on how culture is reflected in the collective process of archiving knowledge on Wikipedia, and demonstrates that cross-lingual interconnections on Wikipedia are not dominated by one powerful language. Our findings also raise some important policy questions for the Wikimedia Foundation.
The proliferation of online social networks in the last decade has not stopped short of pets, and many different online platforms now exist catering to owners of various pets such as cats and dogs. These online pet social networks provide a unique opportunity to study an online social network in which a single user manages multiple user profiles, i.e. one for each pet they own. These types of multi-profile networks allow us to investigate two questions: (1) What is the relationship between the pet-level and human-level network, and (2) what is the relationship between friendship links and family ties? Concretely, we study the online social pet networks Catster, Dogster and Hamsterster, the first two of which are the two largest online pet networks in existence. We show how the networks on the two levels interact, and perform experiments to find out whether knowledge about friendships on a profile-level alone can be used to predict which users are behind which profile. In order to do so, we introduce the concept of multi-profile social network, extend a previously defined spectral test of diagonality to multi-profile networks, define two new homophily measures for multi-profile social networks, perform a two-level social network analysis, and present an algorithm for predicting whether two profiles were created by the same user. As a result, we are able to predict with very high precision whether two profiles were created by a same user. Our work is thus relevant for the analysis of other online communities in which users may use multiple profiles.
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network analysis plays an important role in these domains. A powerful and widespread class of network analysis methods is based on algebraic graph theory, i.e., representing graphs as square adjacency matrices. However, many networks are of a very specific form that clashes with that representation: They are bipartite. That is, they consist of two node types, with each edge connecting a node of one type with a node of the other type. Examples of bipartite networks (also called \emph{two-mode networks}) are persons and the social groups they belong to, musical artists and the musical genres they play, and text documents and the words they contain. In fact, any type of feature that can be represented by a categorical variable can be interpreted as a bipartite network. Although bipartite networks are widespread, most literature in the area of network analysis focuses on unipartite networks, i.e., those networks with only a single type of node. The purpose of this article is to extend a selection of important algebraic network analysis methods to bipartite networks, showing that many methods from algebraic graph theory can be applied to bipartite networks with only minor modifications. We show methods for clustering, visualization and link prediction. Additionally, we introduce new algebraic methods for measuring the bipartivity in near-bipartite graphs.
The prediction of graph evolution is an important and challenging problem in the analysis of networks and of the Web in particular. But while the appearance of new links is part of virtually every model of Web growth, the disappearance of links has received much less attention in the literature. To fill this gap, our approach DecLiNe (an acronym for DECay of LInks in NEtworks) aims to predict link decay in networks, based on structural analysis of corresponding graph models. In analogy to the link prediction problem, we show that analysis of graph structures can help to identify indicators for superfluous links under consideration of common network models. In doing so, we introduce novel metrics that denote the likelihood of certain links in social graphs to remain in the network, and combine them with state-of-the-art machine learning methods for predicting link decay. Our methods are independent of the underlying network type, and can be applied to such diverse networks as the Web, social networks and any other structure representable as a network, and can be easily combined with case-specific content analysis and adopted for a variety of social network mining, filtering and recommendation applications. In systematic evaluations with large-scale datasets of Wikipedia we show the practical feasibility of the proposed structure-based link decay prediction algorithms.
We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.
We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barabási and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent $β$ as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.