Concept lattices with symmetries may be simplified by “folding” them along the orbits of their automorphism group. The resulting diagram is often more intuitive than the full lattice diagram, but well defined annotations are required to make the foldeddiagram as informative as the original one. The folding procedure can be extended to formal contexts.

In this paper we give models and algorithms to describe and analyze the collaboration among authors of Wikipedia from a network analytical perspective. The edit network encodes who interacts how with whom when editing an article; it significantly extends previous network models that code author communities in Wikipedia. Several characteristics summarizing some aspects of the organization process and allowing the analyst to identify certain types of authors can be obtained from the edit network. Moreover, we propose several indicators characterizing the global network structure and methods to visualize edit networks. It is shown that the structural network indicators are correlated with quality labels of the associated Wikipedia articles.

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually project such networks unto simple graphs composed of entities of a single type. In the process, they conflate relations between entities of different types and loose important structural information. We develop a mathematical framework that can be used to compactly represent and analyze heterogeneous networks that combine multiple entity and link types. We generalize Bonacich centrality, which measures connectivity between nodes by the number of paths between them, to heterogeneous networks and use this measure to study network structure. Specifically, we extend the popular modularity-maximization method for community detection to use this centrality metric. We also rank nodes based on their connectivity to other nodes. One advantage of this centrality metric is that it has a tunable parameter we can use to set the length scale of interactions. By studying how rankings change with this parameter allows us to identify important nodes in the network. We apply the proposed method to analyze the structure of several heterogeneous networks. We show that exploiting additional sources of evidence corresponding to links between, as well as among, different entity types yields new insights into network structure.

Social bookmarking systems and their emergent information structures, known as folksonomies, are increasingly important data sources for Semantic Web applications. A key question for harvesting semantics from these systems is how to extend and adapt traditional notions of similarity to folksonomies, and which measures are best suited for applications such as navigation support, semantic search, and ontology learning. Here we build an evaluation framework to compare various general folksonomy-based similarity measures derived from established information-theoretic, statistical, and practical measures. Our framework deals generally and symmetrically with users, tags, and resources. For evaluation purposes we focus on similarity among tags and resources, considering different ways to aggregate annotations across users. After comparing how tag similarity measures predict user-created tag relations, we provide an external grounding by user-validated semantic proxies based on WordNet and the Open Directory. We also investigate the issue of scalability. We ?nd that mutual information with distributional micro-aggregation across users yields the highest accuracy, but is not scalable; per-user projection with collaborative aggregation provides the best scalable approach via incremental computations. The results are consistent across resource and tag similarity.

Operators of online social networks are increasingly sharing potentially sensitive information about users and their relationships with advertisers, application developers, and data-mining researchers. Privacy is typically protected by anonymization, i.e., removing names, addresses, etc. We present a framework for analyzing privacy and anonymity in social networks and develop a new re-identification algorithm targeting anonymized social-network graphs. To demonstrate its effectiveness on real-world networks, we show that a third of the users who can be verified to have accounts on both Twitter, a popular microblogging service, and Flickr, an online photo-sharing site, can be re-identified in the anonymous Twitter graph with only a 12% error rate. Our de-anonymization algorithm is based purely on the network topology, does not require creation of a large number of dummy "sybil" nodes, is robust to noise and all existing defenses, and works even when the overlap between the target network and the adversary's auxiliary information is small.

As online social networking emerges, there has been increased interest to utilize the underlying social structure as well as the available social information to improve search. In this paper, we focus on improving the performance of information collection from the neighborhood of a user in a dynamic social network. To this end, we introduce sampling based algorithms to quickly approximate quantities of interest from the vicinity of a user's social graph. We then introduce and analyze variants of this basic scheme exploring correlations across our samples. Models of centralized and distributed social networks are considered. We show that our algorithms can be utilized to rank items in the neighborhood of a user, assuming that information for each user in the network is available. Using real and synthetic data sets, we validate the results of our analysis and demonstrate the efficiency of our algorithms in approximating quantities of interest. The methods we describe are general and can probably be easily adopted in a variety of strategies aiming to efficiently collect information from a social graph.

We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We examine characteristics and patterns that emerge from the collective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset contains summary properties of 30 billion conversations among 240 million people. From the data, we construct a communication graph with 180 million nodes and 1.3 billion undirected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We investigate on a planetary-scale the oft-cited report that people are separated by "six degrees of separation" and find that the average path length among Messenger users is 6.6. We find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender.

In a social network, nodes correspond topeople or other social entities, and edges correspond to social links between them. In an effort to preserve privacy, the practice of anonymization replaces names with meaningless unique identifiers. We describe a family of attacks such that even from a single anonymized copy of a social network, it is possible for an adversary to learn whether edges exist or not between specific targeted pairs of nodes.

A key argument for modeling knowledge in ontologies is the easy re-use and re-engineering of the knowledge. However, beside consistency checking, current ontology engineering tools provide only basic functionalities for analyzing ontologies. Since ontologies can be considered as (labeled, directed) graphs, graph analysis techniques are a suitable answer for this need. Graph analysis has been performed by sociologists for over 60 years, and resulted in the vivid research area of Social Network Analysis (SNA). While social network structures in general currently receive high attention in the Semantic Web community, there are only very few SNA applications up to now, and virtually none for analyzing the structure of ontologies. We illustrate in this paper the benefits of applying SNA to ontologies and the Semantic Web, and discuss which research topics arise on the edge between the two areas. In particular, we discuss how different notions of centrality describe the core content and structure of an ontology. From the rather simple notion of degree centrality over betweenness centrality to the more complex eigenvector centrality based on Hermitian matrices, we illustrate the insights these measures provide on two ontologies, which are different in purpose, scope, and size.

We describe a novel approach to visualize bibliographic networks that facilitates the simultaneous identification of clusters (e.g., topic areas) and prominent entities (e.g., surveys or landmark papers). While employing the landscape metaphor proposed in several earlier works, we introduce new means to determine relevant parameters of the landscape. Moreover, we are able to compute prominent entities, clustering of entities, and the landscape's surface in a surprisingly simple and uniform way. The effectiveness of our network visualizations is illustrated on data from the graph drawing literature.