Jump to ContentJump to Main Navigation
Show Summary Details
More options …

International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

4 Issues per year


IMPACT FACTOR 2016: 1.420
5-year IMPACT FACTOR: 1.597

CiteScore 2016: 1.81

SCImago Journal Rank (SJR) 2016: 0.524
Source Normalized Impact per Paper (SNIP) 2016: 1.440

Mathematical Citation Quotient (MCQ) 2016: 0.08

Open Access
Online
ISSN
2083-8492
See all formats and pricing
More options …
Volume 25, Issue 2

Issues

Local dependency in networks

Miloš Kudĕlka
  • Corresponding author
  • Department of Computer Science VŠB—Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Šárka Zehnalová
  • Department of Computer Science VŠB—Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Zdenĕk Horák / Pavel Krömer
  • Department of Computer Science VŠB—Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Václav Snášel
  • Department of Computer Science VŠB—Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-06-25 | DOI: https://doi.org/10.1515/amcs-2015-0022

Abstract

Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network’s nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.

Keywords : complex networks; graphs; edge weighting; dependency

References

  • Abdallah, S. (2011). Generalizing unweighted network measures to capture the focus in interactions, Social Network Analysis and Mining 1(4): 255-269.Google Scholar

  • Bar-Yossef, Z. andMashiach, L.-T. (2008). Local approximation of PageRank and reverse PageRank, Proceedings of the 17th ACM Conference on Information and Knowledge Management, Napa Valley, CA, USA, pp. 279-288.Google Scholar

  • Barabási, A.-L. and Frangos, J. (2002). Linked: The New Science of Networks Science Of Networks, Basic Books, New York, NY.Google Scholar

  • Barrat, A., Barthelemy, M., Pastor-Satorras, R. and Vespignani, A. (2004a). The architecture of complex weighted networks, Proceedings of the National Academy of Sciences of the United States of America 101(11): 3747-3752.Web of ScienceGoogle Scholar

  • Barrat, A., Barthélemy, M. and Vespignani, A. (2004b). Weighted evolving networks: coupling topology and weight dynamics, Physical Review Letters 92(22): 228701. CrossrefGoogle Scholar

  • Brin, S. and Page, L. (1998). The anatomy of a large-scale hypertextual web search engine, Proceedings of the 7th International Conference on World Wide Web, Brisbane, Australia, pp. 107-117.Google Scholar

  • Christensen, D. (2005). Fast algorithms for the calculation of Kendall τ , Computational Statistics 20(1): 51-62.CrossrefGoogle Scholar

  • Das Sarma, A., Molla, A., Pandurangan, G. and Upfal, E. (2013). Fast distributed PageRank computation, in D. Frey, M. Raynal, S. Sarkar, R. Shyamasundar and P. Sinha (Eds.), Distributed Computing and Networking, Lecture Notes in Computer Science, Vol. 7730, Springer, Berlin/Heidelberg, pp. 11-26. Google Scholar

  • de Jager, D. (2004). PageRank: Three Distributed Algorithms, Master’s thesis, Imperial College London, London, pubs.doc.ic.ac.uk/pagerank-algorithms/.Google Scholar

  • Farkas, I., Ábel, D., Palla, G. and Vicsek, T. (2007). Weighted network modules, New Journal of Physics 9(6): 180.CrossrefWeb of ScienceGoogle Scholar

  • Fortunato, S. (2010). Community detection in graphs, Physics Reports 486(3): 75-174.Google Scholar

  • Fortunato, S., Boguñá, M., Flammini, A. and Menczer, F. (2008). Approximating PageRank from in-degree, in W. Aiello, A. Broder, J. Janssen and E. Milios (Eds.), Algorithms and Models for the Web-Graph, Springer, Berlin/Heidelberg pp. 59-71.Google Scholar

  • Freeman, L.C. (1979). Centrality in social networks conceptual clarification, Social Networks 1(3): 215-239.CrossrefGoogle Scholar

  • Ghazalpour, A., Doss, S., Zhang, B., Wang, S., Plaisier, C., Castellanos, R., Brozell, A., Schadt, E.E., Drake, T.A., Lusis, A.J. and Horvath, S. (2006). Integrating genetic and network analysis to characterize genes related to mouse weight, PLoS Genetics 2(8): e130.CrossrefGoogle Scholar

  • Han, Y., Zhou, B., Pei, J. and Jia, Y. (2009). Understanding importance of collaborations in co-authorship networks: A supportiveness analysis approach, Proceedings of the 9th SIAM International Conference on Data Mining, Sparks, NV, USA, pp. 1111-1122.Google Scholar

  • Heckerman, D., Chickering, D. M., Meek, C., Rounthwaite, R. and Kadie, C. (2001). Dependency networks for inference, collaborative filtering, and data visualization, The Journal of Machine Learning Research 1: 49-75.Google Scholar

  • Kahanda, I. and Neville, J. (2009). Using transactional information to predict link strength in online social networks, Proceedings of the 3rd International Conference on Weblogs and Social Media (ICWSM), San Jose, CA, USA, pp. 74-81.Google Scholar

  • Kenett, D.Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R.N. and Ben-Jacob, E. (2010). Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market, PLoS One 5(12): e15032. Web of ScienceCrossrefGoogle Scholar

  • Kudelka, M., Horák, Z., Snášel, V., Krömer, P., Platoš, J. and Abraham, A. (2012). Social and swarm aspects of co-authorship network, Logic Journal of IGPL 20(3): 634-643.CrossrefWeb of ScienceGoogle Scholar

  • Langville, A.N. and Meyer, C.D. (2006). Google’s PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton, NJ.Google Scholar

  • Leenders, R.T.A. (2002). Modeling social influence through network autocorrelation: Constructing the weight matrix, Social Networks 24(1): 21-47.CrossrefGoogle Scholar

  • Lin, J. and Dyer, C. (2010). Data-intensive Text Processing with MapReduce, Synthesis Lectures on Human Language Technologies, Morgan & Claypool, San Rafael, CA.Google Scholar

  • Lusseau, D. (2003). The emergent properties of a dolphin social network, Proceedings of the Royal Society of London, Series B: Biological Sciences 270(Suppl 2): S186-S188.CrossrefGoogle Scholar

  • Manaskasemsak, B. and Rungsawang, A. (2004). Parallel PageRank computation on a gigabit PC cluster, 18th International Conference on Advanced Information Networking and Applications, AINA 2004, Fukuoka, Japan, Vol. 1, pp. 273-277.Google Scholar

  • Manaskasemsak, B., Uthayopas, P. and Rungsawang, A. (2006). A mixed MPI-thread approach for parallel page ranking computation, in R. Meersman and Z. Tari (Eds.), Proceedings of the 2006 Confederated International Conference on On the Move to Meaningful Internet Systems: CoopIS, DOA, GADA, and ODBASE, Part II, Springer-Verlag, Berlin/Heidelberg, pp. 1223-1233.Google Scholar

  • Newman, M. (2008). The physics of networks, Physics Today 61(11): 33-38.CrossrefGoogle Scholar

  • Newman, M.E. (2004). Analysis of weighted networks, Physical Review E 70(5): 056131.CrossrefGoogle Scholar

  • Newman, M.E. (2006). Finding community structure in networks using the eigenvectors of matrices, Physical Review E 74(3): 036104.CrossrefGoogle Scholar

  • Nitzberg, B., Schopf, J. and Jones, J. (2004). PBS Pro: Grid computing and scheduling attributes, in J. Nabrzyski, J. Schopf and J. W˛eglarz (Eds.), Grid Resource Management, International Series in Operations Research and Management Science, Vol. 64, Springer, New York, NY, pp. 183-190.Google Scholar

  • Onnela, J.-P., Saramäki, J., Hyvönen, J., Szabó, G., DeMenezes, M. A., Kaski, K., Barabási, A.-L. and Kertész, J. (2007). Analysis of a large-scale weighted network of one-to-one human communication, New Journal of Physics 9(6): 179.CrossrefWeb of ScienceGoogle Scholar

  • Opsahl, T., Agneessens, F. and Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths, Social Networks 32(3): 245-251.Web of ScienceCrossrefGoogle Scholar

  • Opsahl, T. and Panzarasa, P. (2009). Clustering in weighted networks, Social Networks 31(2): 155-163.CrossrefWeb of ScienceGoogle Scholar

  • Plimpton, S.J. and Devine, K.D. (2011). MapReduce in MPI for large-scale graph algorithms, Parallel Computing 37(9): 610-632.CrossrefGoogle Scholar

  • Rungsawang, A. and Manaskasemsak, B. (2003). PageRank computation using PC cluster, in J. Dongarra, D. Laforenza and S. Orlando (Eds.), Recent Advances in Parallel Virtual Machine and Message Passing Interface, Lecture Notes in Computer Science, Vol. 2840, Springer Berlin/Heidelberg, pp. 152-159.Google Scholar

  • Sankaralingam, K., Sethumadhavan, S. and Browne, J. (2003). Distributed PageRank for P2P systems, 12th IEEE International Symposium on High Performance Distributed Computing, 2003, Seattle, WA, USA, pp. 58-68.Google Scholar

  • Wiedermann, M., Donges, J.F., Heitzig, J. and Kurths, J. (2013). Node-weighted interacting network measures improve the representation of real-world complex systems, Europhysics Letters 102(2): 28007.CrossrefGoogle Scholar

  • Witten, I.H., Gori, M. and Numerico, T. (2006). Web Dragons: Inside the Myths of Search Engine Technology, Morgan Kaufmann, San Francisco, CA. Zachary, W.W. (1977). An information flow model for conflict and fission in small groups, Journal of Anthropological Research 33(4): 452-473.Google Scholar

  • Zehnalova, S., Horak, Z., Kudelka, M. and Snael, V. (2013). Local dependency in networks, 5th International Conference on Intelligent Networking and Collaborative Systems (INCoS), Xi’an, China, pp. 250-254.Google Scholar

  • Zhang, B. and Horvath, S. (2005). A general framework for weighted gene co-expression network analysis, Statistical Applications in Genetics and Molecular Biology 4(1): 1128.Google Scholar

  • Zhu, Y., Ye, S. and Li, X. (2005). Distributed PageRank computation based on iterative aggregation-disaggregation methods, Proceedings of the 14th ACM International Conference on Information and Knowledge Management, CIKM’05, Bremen, Germany, pp. 578-585. Google Scholar

About the article

Received: 2014-02-04

Revised: 2014-08-08

Published Online: 2015-06-25

Published in Print: 2015-06-01


Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 25, Issue 2, Pages 281–293, ISSN (Online) 2083-8492, DOI: https://doi.org/10.1515/amcs-2015-0022.

Export Citation

© by Miloš Kudĕlka. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Martín Cera and Eugenio M. Fedriani
International Journal of Applied Mathematics and Computer Science, 2016, Volume 26, Number 4

Comments (0)

Please log in or register to comment.
Log in