@inproceedings{giatsidis2011evaluating,
  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.},
  author = {Giatsidis, Christos and Thilikos, Dimitrios M. and Vazirgiannis, Michalis},
  booktitle = {Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on},
  doi = {10.1109/ASONAM.2011.65},
  interhash = {ccc1059e51e6c0671f9987824e7c9f92},
  intrahash = {e635975e729c3aee7575db0485f3e853},
  pages = {87-93},
  title = {Evaluating Cooperation in Communities with the k-Core Structure},
  url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5992567&tag=1},
  year = 2011
}

@inproceedings{doerfel2013analysis,
  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.},
  acmid = {2507222},
  address = {New York, NY, USA},
  author = {Doerfel, Stephan and Jäschke, Robert},
  booktitle = {Proceedings of the 7th ACM conference on Recommender systems},
  doi = {10.1145/2507157.2507222},
  interhash = {3eaf2beb1cdad39b7c5735a82c3338dd},
  intrahash = {a73213a865503252caa4b28e88a77108},
  isbn = {978-1-4503-2409-0},
  location = {Hong Kong, China},
  numpages = {4},
  pages = {343--346},
  publisher = {ACM},
  series = {RecSys '13},
  title = {An Analysis of Tag-Recommender Evaluation Procedures},
  url = {http://doi.acm.org/10.1145/2507157.2507222},
  year = 2013
}

@article{journals/corr/cs-DS-0202039,
  author = {Batagelj, Vladimir and Zaversnik, Matjaz},
  ee = {http://arxiv.org/abs/cs.DS/0202039},
  interhash = {775d7337332536953aaac48aedae1a68},
  intrahash = {f89e52052c37bd78302c1438d5344324},
  journal = {CoRR},
  title = {Generalized Cores},
  url = {http://dblp.uni-trier.de/db/journals/corr/corr0202.html#cs-DS-0202039},
  volume = {cs.DS/0202039},
  year = 2002
}

@inproceedings{ahmed2007visualisation,
  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.},
  author = {Ahmed, Adel and Batagelj, Vladimir and Fu, Xiaoyan and Hong, Seok-Hee and Merrick, Damian and Mrvar, Andrej},
  booktitle = {Visualization, 2007. APVIS '07. 2007 6th International Asia-Pacific Symposium on},
  doi = {10.1109/APVIS.2007.329304},
  interhash = {98c887b94e1826332d7739e3af78265e},
  intrahash = {4ce8ac41630e50a8447bd969ec1219da},
  month = {feb.},
  pages = {17 -24},
  title = {Visualisation and analysis of the internet movie database},
  url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4126213&tag=1},
  year = 2007
}

@article{batagelj2011algorithms,
  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 $${\mathcal{O}(m)}$$, 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 $${\mathcal{O}(m\cdot\max(\Delta,\log{n}))}$$ 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.},
  address = {Berlin / Heidelberg},
  affiliation = {Department of Mathematics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia},
  author = {Batagelj, Vladimir and Zaveršnik, Matjaž},
  doi = {10.1007/s11634-010-0079-y},
  interhash = {a0bd7331f81bb4da72ce115d5943d6e4},
  intrahash = {cd0d5266688af6bb98bde7f99e3a54c1},
  issn = {1862-5347},
  journal = {Advances in Data Analysis and Classification},
  keyword = {Mathematics and Statistics},
  number = 2,
  pages = {129-145},
  publisher = {Springer},
  title = {Fast algorithms for determining (generalized) core groups in social networks},
  url = {http://dx.doi.org/10.1007/s11634-010-0079-y},
  volume = 5,
  year = 2011
}

@incollection{batagelj1999partitioning,
  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.},
  address = {Berlin / Heidelberg},
  affiliation = {FMF, Department of Mathematics, and IMFM Department of Theoretical Computer Science University of Ljubljana Jadranska 19 1000 Ljubljana Slovenia},
  author = {Batagelj, Vladimir and Mrvar, Andrej and Zaveršnik, Matjaž},
  booktitle = {Graph Drawing},
  doi = {10.1007/3-540-46648-7_9},
  editor = {Kratochvíyl, Jan},
  interhash = {223ade3dd692bb262a6398e1442b4dfd},
  intrahash = {2e005638761fc15757dd18113783aa97},
  isbn = {978-3-540-66904-3},
  keyword = {Computer Science},
  pages = {90-97},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Partitioning Approach to Visualization of Large Graphs},
  url = {http://dx.doi.org/10.1007/3-540-46648-7_9},
  volume = 1731,
  year = 1999
}

@misc{batagelj2003algorithm,
  abstract = {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.},
  author = {Batagelj, V. and Zaversnik, M.},
  interhash = {63be428635128d4eebd095e2ca44cdf2},
  intrahash = {d533733cd010732a5ca81417f4deca0a},
  note = {cite arxiv:cs/0310049},
  title = {An O(m) Algorithm for Cores Decomposition of Networks},
  url = {http://arxiv.org/abs/cs/0310049},
  year = 2003
}

@article{seidman1983network,
  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.},
  author = {Seidman, Stephen B.},
  doi = {10.1016/0378-8733(83)90028-X},
  interhash = {bdba8b78574faec3a7315423e29b7556},
  intrahash = {402ff073bdbfef97765e307068f59110},
  issn = {0378-8733},
  journal = {Social Networks},
  number = 3,
  pages = {269 - 287},
  title = {Network structure and minimum degree},
  url = {http://www.sciencedirect.com/science/article/pii/037887338390028X},
  volume = 5,
  year = 1983
}

@misc{batagelj2002generalized,
  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 $O(m
\max (\Delta, \log n))$ time.},
  author = {Batagelj, Vladimir and Zaveršnik, Matjaž},
  interhash = {909808bf89a41bbb2c292ebf66315398},
  intrahash = {7951390a09c2a2f7991bfbaba9877ff5},
  note = {cite arxiv:cs/0202039},
  title = {Generalized Cores},
  url = {http://arxiv.org/abs/cs/0202039},
  year = 2002
}

@article{Duq,
  address = {Amsterdam, The Netherlands, The Netherlands},
  author = {Duquenne, Vincent},
  doi = {http://dx.doi.org/10.1016/0012-365X(91)90043-2},
  interhash = {3fcc87180a838828f74fd82d7b6ac209},
  intrahash = {6c41ab93d9468e2b180b0d1a189c2cb8},
  issn = {0012-365X},
  journal = {Discrete Math.},
  number = {2-3},
  pages = {133--147},
  publisher = {Elsevier Science Publishers B. V.},
  title = {The core of finite lattices},
  volume = 87,
  year = 1991
}

@article{Duquenne1991133,
  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.},
  author = {Duquenne, Vincent},
  doi = {10.1016/0012-365X(91)90005-M},
  interhash = {3fcc87180a838828f74fd82d7b6ac209},
  intrahash = {3754f36ef7da2a619c34a7c863ba3427},
  issn = {0012-365X},
  journal = {Discrete Mathematics},
  number = {2-3},
  pages = {133 - 147},
  title = {The core of finite lattices},
  url = {http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d},
  volume = 88,
  year = 1991
}

@article{jaeschke2008tag,
  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 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.
},
  address = {Amsterdam},
  author = {Jäschke, Robert and Marinho, Leandro and Hotho, Andreas and Schmidt-Thieme, Lars and Stumme, Gerd},
  doi = {10.3233/AIC-2008-0438},
  editor = {Giunchiglia, Enrico},
  interhash = {b2f1aba6829affc85d852ea93a8e39f7},
  intrahash = {955bcf14f3272ba6eaf3dadbef6c0b10},
  issn = {0921-7126},
  journal = {AI Communications},
  number = 4,
  pages = {231-247},
  publisher = {IOS Press},
  title = {Tag Recommendations in Social Bookmarking Systems},
  url = {http://dx.doi.org/10.3233/AIC-2008-0438},
  vgwort = {63},
  volume = 21,
  year = 2008
}