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.

@inproceedings{doerfel2013analysis, author = {Doerfel, Stephan and Jäschke, Robert}, title = {An Analysis of Tag-Recommender Evaluation Procedures}, booktitle = {Proceedings of the 7th ACM conference on Recommender systems}, series = {RecSys '13}, publisher = {ACM}, address = {New York, NY, USA}, year = {2013}, pages = {343--346}, url = {http://doi.acm.org/10.1145/2507157.2507222}, doi = {10.1145/2507157.2507222}, isbn = {978-1-4503-2409-0}, keywords = {2013, BibSonomy, core, evaluation, iteg, itegpub, l3s, myown, recsys, tag}, abstract = {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.} }

%0 = inproceedings %A = Doerfel, Stephan and Jäschke, Robert %B = Proceedings of the 7th ACM conference on Recommender systems %C = New York, NY, USA %D = 2013 %I = ACM %T = An Analysis of Tag-Recommender Evaluation Procedures %U = http://doi.acm.org/10.1145/2507157.2507222

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.

@inproceedings{doerfel2013analysis, author = {Doerfel, Stephan and Jäschke, Robert}, title = {An analysis of tag-recommender evaluation procedures}, booktitle = {Proceedings of the 7th ACM conference on Recommender systems}, series = {RecSys '13}, publisher = {ACM}, address = {New York, NY, USA}, year = {2013}, pages = {343--346}, url = {https://www.kde.cs.uni-kassel.de/pub/pdf/doerfel2013analysis.pdf}, doi = {10.1145/2507157.2507222}, isbn = {978-1-4503-2409-0}, keywords = {2013, bibsonomy, bookmarking, collaborative, core, evaluation, folkrank, folksonomy, graph, iteg, itegpub, l3s, recommender, social, tagging}, abstract = {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.} }

%0 = inproceedings %A = Doerfel, Stephan and Jäschke, Robert %B = Proceedings of the 7th ACM conference on Recommender systems %C = New York, NY, USA %D = 2013 %I = ACM %T = An analysis of tag-recommender evaluation procedures %U = https://www.kde.cs.uni-kassel.de/pub/pdf/doerfel2013analysis.pdf

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.

@inproceedings{doerfel2013analysis, author = {Doerfel, Stephan and Jäschke, Robert}, title = {An Analysis of Tag-Recommender Evaluation Procedures}, booktitle = {Proceedings of the 7th ACM conference on Recommender systems}, series = {RecSys '13}, publisher = {ACM}, address = {New York, NY, USA}, year = {2013}, pages = {343--346}, url = {http://doi.acm.org/10.1145/2507157.2507222}, doi = {10.1145/2507157.2507222}, isbn = {978-1-4503-2409-0}, keywords = {2013, BibSonomy, core, evaluation, myown, recsys, tag}, abstract = {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.} }

%0 = inproceedings %A = Doerfel, Stephan and Jäschke, Robert %B = Proceedings of the 7th ACM conference on Recommender systems %C = New York, NY, USA %D = 2013 %I = ACM %T = An Analysis of Tag-Recommender Evaluation Procedures %U = http://doi.acm.org/10.1145/2507157.2507222

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 “

@article{batagelj2011algorithms, author = {Batagelj, Vladimir and Zaveršnik, Matjaž}, title = {Fast algorithms for determining (generalized) core groups in social networks}, journal = {Advances in Data Analysis and Classification}, publisher = {Springer}, year = {2011}, volume = {5}, number = {2}, pages = {129--145}, url = {http://dx.doi.org/10.1007/s11634-010-0079-y}, doi = {10.1007/s11634-010-0079-y}, issn = {1862-5347}, keywords = {analysis, core, network, sna, social}, abstract = {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 “} }

%0 = article %A = Batagelj, Vladimir and Zaveršnik, Matjaž %D = 2011 %I = Springer %T = Fast algorithms for determining (generalized) core groups in social networks %U = http://dx.doi.org/10.1007/s11634-010-0079-y

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.

@article{batagelj2011algorithms, author = {Batagelj, Vladimir and Zaveršnik, Matjaž}, title = {Fast algorithms for determining (generalized) core groups in social networks}, journal = {Advances in Data Analysis and Classification}, publisher = {Springer}, address = {Berlin / Heidelberg}, year = {2011}, volume = {5}, number = {2}, pages = {129-145}, url = {http://dx.doi.org/10.1007/s11634-010-0079-y}, doi = {10.1007/s11634-010-0079-y}, issn = {1862-5347}, keywords = {core, graph}, abstract = {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.} }

%0 = article %A = Batagelj, Vladimir and Zaveršnik, Matjaž %C = Berlin / Heidelberg %D = 2011 %I = Springer %T = Fast algorithms for determining (generalized) core groups in social networks %U = http://dx.doi.org/10.1007/s11634-010-0079-y

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.

@inproceedings{giatsidis2011evaluating, author = {Giatsidis, Christos and Thilikos, Dimitrios M. and Vazirgiannis, Michalis}, title = {Evaluating Cooperation in Communities with the k-Core Structure}, booktitle = {Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on}, year = {2011}, pages = {87-93}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5992567&tag=1}, doi = {10.1109/ASONAM.2011.65}, keywords = {community, core, k-core}, abstract = {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.} }

%0 = inproceedings %A = Giatsidis, Christos and Thilikos, Dimitrios M. and Vazirgiannis, Michalis %B = Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on %D = 2011 %T = Evaluating Cooperation in Communities with the k-Core Structure %U = http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5992567&tag=1

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.
this paper we evaluate and compare several recommendation algorithms on large-scale real life datasets: an adaptation of
er-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.

@article{jaeschke2008tag, author = {Jäschke, Robert and Marinho, Leandro and Hotho, Andreas and Schmidt-Thieme, Lars and Stumme, Gerd}, title = {Tag Recommendations in Social Bookmarking Systems}, editor = {Giunchiglia, Enrico}, journal = {AI Communications}, publisher = {IOS Press}, address = {Amsterdam}, year = {2008}, volume = {21}, number = {4}, pages = {231-247}, url = {http://dx.doi.org/10.3233/AIC-2008-0438}, doi = {10.3233/AIC-2008-0438}, issn = {0921-7126}, keywords = {bookmark, core, folkrank, folksonomy, recommendations, social, tag}, abstract = {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 ofuser-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.} }

%0 = article %A = Jäschke, Robert and Marinho, Leandro and Hotho, Andreas and Schmidt-Thieme, Lars and Stumme, Gerd %C = Amsterdam %D = 2008 %I = IOS Press %T = Tag Recommendations in Social Bookmarking Systems %U = http://dx.doi.org/10.3233/AIC-2008-0438

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.

@inproceedings{ahmed2007visualisation, author = {Ahmed, Adel and Batagelj, Vladimir and Fu, Xiaoyan and Hong, Seok-Hee and Merrick, Damian and Mrvar, Andrej}, title = {Visualisation and analysis of the internet movie database}, booktitle = {Visualization, 2007. APVIS '07. 2007 6th International Asia-Pacific Symposium on}, year = {2007}, pages = {17 -24}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4126213&tag=1}, doi = {10.1109/APVIS.2007.329304}, keywords = {analysis, core, imdb}, abstract = {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.} }

%0 = inproceedings %A = Ahmed, Adel and Batagelj, Vladimir and Fu, Xiaoyan and Hong, Seok-Hee and Merrick, Damian and Mrvar, Andrej %B = Visualization, 2007. APVIS '07. 2007 6th International Asia-Pacific Symposium on %D = 2007 %T = Visualisation and analysis of the internet movie database %U = http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4126213&tag=1

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.

@inproceedings{baur2007generating, author = {Baur, Michael and Gaertler, Marco and Görke, Robert and Krug, Marcus and Wagner, Dorothea}, title = {Generating Graphs with Predefined k-Core Structure}, booktitle = {Proceedings of the European Conference of Complex Systems}, year = {2007}, url = {http://i11www.ira.uka.de/extra/publications/bggkw-ggpcs-07.pdf}, keywords = {analysis, core, generator, graph, structure}, abstract = {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. } }

%0 = inproceedings %A = Baur, Michael and Gaertler, Marco and Görke, Robert and Krug, Marcus and Wagner, Dorothea %B = Proceedings of the European Conference of Complex Systems %D = 2007 %T = Generating Graphs with Predefined k-Core Structure %U = http://i11www.ira.uka.de/extra/publications/bggkw-ggpcs-07.pdf

@techreport{behrisch2007order, author = {Behrisch, Michael and Coja-Oghlan, Amin and Kang, Mihyun}, title = {The order of the giant component of random hypergraphs}, year = {2007}, url = {http://www.informatik.hu-berlin.de/~coja/jlimit7.pdf}, keywords = {core, giant, hypergraph, kcore, order, random} }

%0 = techreport %A = Behrisch, Michael and Coja-Oghlan, Amin and Kang, Mihyun %B = } %C = %D = 2007 %I = %T = The order of the giant component of random hypergraphs} %U = http://www.informatik.hu-berlin.de/~coja/jlimit7.pdf

@misc{alvarezhamelin-2005, author = {Alvarez-Hamelin, Jose Ignacio and Dall'Asta, Luca and Barrat, Alain and Vespignani, Alessandro}, title = {k-core decomposition: a tool for the analysis of large scale Internet graphs}, year = {2005}, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0511007}, keywords = {analysis, core, decomposition, graph, kcore, network, toread} }

%0 = misc %A = Alvarez-Hamelin, Jose Ignacio and Dall'Asta, Luca and Barrat, Alain and Vespignani, Alessandro %B = } %C = %D = 2005 %I = %T = k-core decomposition: a tool for the analysis of large scale Internet graphs} %U = http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0511007

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

@misc{batagelj2003algorithm, author = {Batagelj, V. and Zaversnik, M.}, title = {An O(m) Algorithm for Cores Decomposition of Networks}, year = {2003}, note = {cite arxiv:cs/0310049}, url = {http://arxiv.org/abs/cs/0310049}, keywords = {core, graph, network}, abstract = {The structure of large networks can be revealed by partitioning them tosmaller parts, which are easier to handle. One of such decompositions is basedon $k$--cores, proposed in 1983 by Seidman. In the paper an efficient, $O(m)$,$m$ is the number of lines, algorithm for determining the cores decompositionof a given network is presented.} }

%0 = misc %A = Batagelj, V. and Zaversnik, M. %B = } %C = %D = 2003 %I = %T = An O(m) Algorithm for Cores Decomposition of Networks} %U = http://arxiv.org/abs/cs/0310049

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.

@article{batagelj2002generalized, author = {Batagelj, V. and Zaversnik, M.}, title = {Generalized Cores}, journal = {CoRR}, year = {2002}, volume = {cs.DS/0202039}, url = {http://arxiv.org/abs/cs/0202039}, keywords = {analysis, core, generalized, graph, kcore, network}, abstract = {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.} }

%0 = article %A = Batagelj, V. and Zaversnik, M. %D = 2002 %T = Generalized Cores %U = http://arxiv.org/abs/cs/0202039

@article{journals/corr/cs-DS-0202039, author = {Batagelj, Vladimir and Zaversnik, Matjaz}, title = {Generalized Cores}, journal = {CoRR}, year = {2002}, volume = {cs.DS/0202039}, url = {http://dblp.uni-trier.de/db/journals/corr/corr0202.html#cs-DS-0202039}, keywords = {core, generalized, p-core} }

%0 = article %A = Batagelj, Vladimir and Zaversnik, Matjaz %D = 2002 %T = Generalized Cores %U = http://dblp.uni-trier.de/db/journals/corr/corr0202.html#cs-DS-0202039

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

@misc{batagelj2002generalized, author = {Batagelj, Vladimir and Zaveršnik, Matjaž}, title = {Generalized Cores}, year = {2002}, note = {cite arxiv:cs/0202039}, url = {http://arxiv.org/abs/cs/0202039}, keywords = {core, generalized, p-core}, abstract = {Cores are, besides connectivity components, one among few concepts thatprovides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based onvertex property function is presented. It is shown that for the local monotonevertex property functions the corresponding cores can be determined in $O(mmax( logn))$ time.} }

%0 = misc %A = Batagelj, Vladimir and Zaveršnik, Matjaž %B = } %C = %D = 2002 %I = %T = Generalized Cores} %U = http://arxiv.org/abs/cs/0202039

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.

@incollection{batagelj1999partitioning, author = {Batagelj, Vladimir and Mrvar, Andrej and Zaveršnik, Matjaž}, title = {Partitioning Approach to Visualization of Large Graphs}, editor = {Kratochvíyl, Jan}, booktitle = {Graph Drawing}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, address = {Berlin / Heidelberg}, year = {1999}, volume = {1731}, pages = {90-97}, url = {http://dx.doi.org/10.1007/3-540-46648-7_9}, doi = {10.1007/3-540-46648-7_9}, isbn = {978-3-540-66904-3}, keywords = {core, graph}, abstract = {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.} }

%0 = incollection %A = Batagelj, Vladimir and Mrvar, Andrej and Zaveršnik, Matjaž %B = Graph Drawing %C = Berlin / Heidelberg %D = 1999 %I = Springer %T = Partitioning Approach to Visualization of Large Graphs %U = http://dx.doi.org/10.1007/3-540-46648-7_9

@article{Duq, author = {Duquenne, Vincent}, title = {The core of finite lattices}, journal = {Discrete Math.}, publisher = {Elsevier Science Publishers B. V.}, address = {Amsterdam, The Netherlands, The Netherlands}, year = {1991}, volume = {87}, number = {2-3}, pages = {133--147}, doi = {http://dx.doi.org/10.1016/0012-365X(91)90043-2}, issn = {0012-365X}, keywords = {cited, core, da, diplomarbeit, finite, lattice, scaffolding} }

%0 = article %A = Duquenne, Vincent %C = Amsterdam, The Netherlands, The Netherlands %D = 1991 %I = Elsevier Science Publishers B. V. %T = The core of finite lattices

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.

@article{Duquenne1991133, author = {Duquenne, Vincent}, title = {The core of finite lattices}, journal = {Discrete Mathematics}, year = {1991}, volume = {88}, number = {2-3}, pages = {133 - 147}, url = {http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d}, doi = {10.1016/0012-365X(91)90005-M}, issn = {0012-365X}, keywords = {core, fca, lattice, scaffolding}, abstract = {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.} }

%0 = article %A = Duquenne, Vincent %D = 1991 %T = The core of finite lattices %U = http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d

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.

@article{seidman1983network, author = {Seidman, Stephen B.}, title = {Network structure and minimum degree}, journal = {Social Networks}, year = {1983}, volume = {5}, number = {3}, pages = {269 - 287}, url = {http://www.sciencedirect.com/science/article/pii/037887338390028X}, doi = {10.1016/0378-8733(83)90028-X}, issn = {0378-8733}, keywords = {core, graph, network}, abstract = {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.} }

%0 = article %A = Seidman, Stephen B. %D = 1983 %T = Network structure and minimum degree %U = http://www.sciencedirect.com/science/article/pii/037887338390028X