Cerinšek, M. & Batagelj, V. (2015), 'Network analysis of Zentralblatt MATH data', Scientometrics 102 (1) , 977-1001 .
[BibTeX] [Endnote]

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 .
[BibTeX] [Endnote]

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.

2009

BATAGELJ, V. (2009), 'Social Network Analysis, Large-scale', Encyclopedia of Complexity and System Science .
[BibTeX] [Endnote]

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 .
[BibTeX] [Endnote]

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.

2005

de Nooy, W.; Mrvar, A. & Batagelj, V. (2005), Exploratory Social Network Analysis with Pajek , Cambridge University Press , New York, NY, USA .
[BibTeX] [Endnote]

de Nooy, W.; Mrvar, A. & Batagelj, V. (2005), Exploratory Social Network Analysis with Pajek (Structural Analysis in the Social Sciences) , Cambridge University Press .
[BibTeX] [Endnote]

2002

Batagelj, V. & Zaversnik, M. (2002), 'Generalized Cores', CoRR cs.DS/0202039 .
[BibTeX] [Endnote]

Batagelj, V. & Zaveršnik, M. (2002), 'Generalized Cores' , cite arxiv:cs/0202039 .
[BibTeX] [Endnote]

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 .
[BibTeX] [Endnote]

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.