Abstract
We are proposing in this paper a more general network modeling framework for complex system representation by introducing Stochastic Pretopology, a result of the combination of Pretopology theory and Random Sets. After giving the definition and some examples for building stochastic pretopology in many situations, we show how this approach generalizes graph, random graph, multi-relational networks and we present an application by giving Pretopology Cascade Model as a general model for information diffusion process that can take place in more complex networks such as multi-relational networks or stochastic graphs.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Basileu, C., Amor, S.B., Bui, M., Lamure, M.: Prétopologie stochastique et réseaux complexes. Stud. Inform. Univ. 10(2), 73–138 (2012)
Belmandt, Z.: Basics of Pretopology. Hermann (2011)
Berge, C.: The Theory of Graphs. Courier Corporation (1962)
Bui, Q.V., Sayadi, K., Bui, M.: A multi-criteria document clustering method based on topic modeling and pseudoclosure function. Informatica 40(2), 169–180 (2016)
Easley, D., Kleinberg, J.: Networks Crowds and Markets. Cambridge University Press, Cambridge (2010)
Goldenberg, J., Libai, B., Muller, E.: Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark. Lett. 12(3), 211–223 (2001)
Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)
Lamure, M., Bonnevay, S., Bui, M., Amor, S.B.: A stochastic and pretopological modeling aerial pollution of an urban area. Stud. Inform. Univ. 7(3), 410–426 (2009)
Molchanov, I.: Theory of Random Sets. Springer, London (2005). https://doi.org/10.1007/1-84628-150-4
Newman, M.E.: Complex systems: a survey. Am. J. Phys. 79, 800–810 (2011)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)
Nguyen, H.T.: An Introduction to Random Sets. CRC Press, Boca Raton (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Bui, Q.V., Ben Amor, S., Bui, M. (2018). Stochastic Pretopology as a Tool for Topological Analysis of Complex Systems. In: Nguyen, N., Hoang, D., Hong, TP., Pham, H., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2018. Lecture Notes in Computer Science(), vol 10752. Springer, Cham. https://doi.org/10.1007/978-3-319-75420-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-75420-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-75419-2
Online ISBN: 978-3-319-75420-8
eBook Packages: Computer ScienceComputer Science (R0)