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Projects / Programmes source: ARIS

Very large graphs and networks

Research activity

Code Science Field Subfield
1.01.05  Natural sciences and mathematics  Mathematics  Graph theory 

Code Science Field
P001  Natural sciences and mathematics  Mathematics 

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
mathematics, graph theory, networks, graph limits, structure of data, spectral method, topological structures on graphs.
Evaluation (rules)
source: COBISS
Researchers (14)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  25993  PhD Sergio Cabello Justo  Mathematics  Researcher  2011 - 2014  218 
2.  16332  PhD Gašper Fijavž  Mathematics  Researcher  2011 - 2014  121 
3.  24751  PhD Janja Jerebic  Administrative and organisational sciences  Researcher  2011 - 2014  121 
4.  11220  PhD Martin Juvan  Mathematics  Researcher  2011 - 2012  235 
5.  05949  PhD Sandi Klavžar  Mathematics  Researcher  2011 - 2014  1,179 
6.  22401  PhD Matjaž Konvalinka  Mathematics  Researcher  2011 - 2013  118 
7.  31670  PhD Borut Lužar  Computer intensive methods and applications  Researcher  2011 - 2014  184 
8.  01931  PhD Bojan Mohar  Mathematics  Head  2011 - 2014  1,002 
9.  22649  PhD Janez Povh  Computer intensive methods and applications  Researcher  2013 - 2014  342 
10.  15518  PhD Riste Škrekovski  Mathematics  Researcher  2011 - 2014  507 
11.  24904  PhD Simon Špacapan  Mathematics  Researcher  2011 - 2014  109 
12.  23904  PhD Aleksandra Tepeh  Mathematics  Researcher  2011 - 2013  132 
13.  24049  PhD Andrej Vodopivec  Mathematics  Researcher  2011 - 2014  14 
14.  18504  PhD Petra Žigert Pleteršek  Mathematics  Researcher  2011 - 2014  174 
Organisations (3)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,263 
2.  1554  University of Ljubljana, Faculty of Mathematics and Physics  Ljubljana  1627007  34,291 
3.  2547  University of Maribor, Faculty of natural sciences and mathematics  Maribor  5089638051  18,078 
Abstract
Our main concern will be the study of very large graphs, the main theme being the relationship between local and global properties. There is need for basic theory, although the case of dense graphs (Lovasz, Szegedy, Borgs, Chayes, Sos, Vesztergombi) and, at the other extreme, the case of planar graphs (Schramm, Angel, LeGall, Marckert in Mokkadem) are well understood. Our goal is to discover and use connections between analytic, algebraic and topological properties of large graphs. The main themes are convergence and limits of graphs embedded in surfaces, graphs in other minor-closed families, application of nonstandard analysis (Gromov-Hausdorff metric) for comparison of large objects, theory of probabilistic algorithms based on local observations, study of products and bundles and development of fundamental algorithms for large graphs.
Significance for science
The project belongs to basic research from the area of mathematics. Problems that we work on are internationally important, which can in particular be justified with our bibliography from the last period as well as with the (citation) impact of our results. The problems are central in the area of modern graph theory. Our newly obtained results have been published in established international journals and are presented at international scientific conferences. For the next period we expect that we will be invited to deliver several invited plenary talks which will further emphasize the visibility of our research achievements. In this way we will further increase the role of the Slovenian graph theory school.
Significance for the country
The results obtained are mostly theoretical. Nevertheless, some of our results have a potential for applications which is in particular the case with our research in algorithmic and optimization aspects of graph theory. The area of "big data" and hence also our main theme of large graphs is one of the priorities listed in the research policy documents worldwide.
Most important scientific results Annual report 2011, 2012, 2013, final report, complete report on dLib.si
Most important socioeconomically and culturally relevant results Annual report 2011, 2012, 2013, final report, complete report on dLib.si
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