Doerfel, S. & Jäschke, R. (2013), An Analysis of Tag-Recommender Evaluation Procedures, in 'Proceedings of the 7th ACM conference on Recommender systems' , ACM, New York, NY, USA , pp. 343--346 .
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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.

Doerfel, S. & Jäschke, R. (2013), An analysis of tag-recommender evaluation procedures, in 'Proceedings of the 7th ACM conference on Recommender systems' , ACM, New York, NY, USA , pp. 343--346 .
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Batagelj, V. & Zaveršnik, M. (2011), 'Fast algorithms for determining (generalized) core groups in social networks', Advances in Data Analysis and Classification 5 (2) , 129--145 .
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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.

Giatsidis, C.; Thilikos, D. M. & Vazirgiannis, M. (2011), Evaluating Cooperation in Communities with the k-Core Structure, in 'Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on' , pp. 87-93 .
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Community sub graphs are characterized by dense connections or interactions among its nodes. Community detection and evaluation is an important task in graph mining. A variety of measures have been proposed to evaluate the quality of such communities. In this paper, we evaluate communities based on the k-core concept, as means of evaluating their collaborative nature - a property not captured by the single node metrics or by the established community evaluation metrics. Based on the k-core, which essentially measures the robustness of a community under degeneracy, we extend it to weighted graphs, devising a novel concept of k-cores on weighted graphs. We applied the k-core approach on large real world graphs - such as DBLP and report interesting results.

2008

Jäschke, R.; Marinho, L.; Hotho, A.; Schmidt-Thieme, L. & Stumme, G. (2008), 'Tag Recommendations in Social Bookmarking Systems', AI Communications 21 (4) , 231-247 .
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Collaborative tagging systems allow users to assign keywords - so called "tags" - to resources. Tags are used for navigation, finding resources and serendipitous browsing and thus provide an immediate benefit for users. These systems usually include tag recommendation mechanisms easing the process of finding good tags for a resource, but also consolidating the tag vocabulary across users. In practice, however, only very basic recommendation strategies are applied. In this paper we evaluate and compare several recommendation algorithms on large-scale real life datasets: an adaptation of user-based collaborative filtering, a graph-based recommender built on top of the FolkRank algorithm, and simple methods based on counting tag occurences. We show that both FolkRank and Collaborative Filtering provide better results than non-personalized baseline methods. Moreover, since methods based on counting tag occurrences are computationally cheap, and thus usually preferable for real time scenarios, we discuss simple approaches for improving the performance of such methods. We show, how a simple recommender based on counting tags from users and resources can perform almost as good as the best recommender.

2007

Ahmed, A.; Batagelj, V.; Fu, X.; Hong, S.-H.; Merrick, D. & Mrvar, A. (2007), Visualisation and analysis of the internet movie database, in 'Visualization, 2007. APVIS '07. 2007 6th International Asia-Pacific Symposium on' , pp. 17 -24 .
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In this paper, we present a case study for the visualisation and analysis of large and complex temporal multivariate networks derived from the Internet movie database (IMDB). Our approach is to integrate network analysis methods with visualisation in order to address scalability and complexity issues. In particular, we defined new analysis methods such as (p,q)-core and 4-ring to identify important dense subgraphs and short cycles from the huge bipartite graphs. We applied island analysis for a specific time slice in order to identify important and meaningful subgraphs. Further, a temporal Kevin Bacon graph and a temporal two mode network are extracted in order to provide insight and knowledge on the evolution.

Baur, M.; Gaertler, M.; Görke, R.; Krug, M. & Wagner, D. (2007), Generating Graphs with Predefined k-Core Structure, in 'Proceedings of the European Conference of Complex Systems' .
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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.

2005

Alvarez-Hamelin, J. I.; Dall'Asta, L.; Barrat, A. & Vespignani, A. (2005), 'k-core decomposition: a tool for the analysis of large scale Internet graphs' .
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2003

Batagelj, V. & Zaversnik, M. (2003), 'An O(m) Algorithm for Cores Decomposition of Networks' , cite arxiv:cs/0310049 .
[Volltext] [Kurzfassung] [BibTeX] [Endnote]

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.

2002

Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in $O(m max( logn))$ time.

1999

Batagelj, V.; Mrvar, A. & Zaveršnik, M. (1999), Partitioning Approach to Visualization of Large Graphs, in Jan Kratochvíyl, ed., 'Graph Drawing' , Springer, Berlin / Heidelberg , pp. 90-97 .
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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.

1991

The meet-core of a finite lattice L is its minimal -- in fact minimum -- partial meet- subsemilattice of which the filter lattice is isomorphic to L. This gives a representation theory for finite lattices, in particular which extends Birkhoff's correspondence between ordered sets and distributive lattices, and is linked with Wille's notion of scaffolding. The meet-cores (and dually the join-cores) of modular, geometric and join-meet-distributive lattices are characterized locally by some obligatory sublattices or by some construction procedures otherwise.

1983

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.