publication . Article . Other literature type . Preprint . 2019

Scale-variant topological information for characterizing the structure of complex networks.

Tran, Quoc Hoan; Vo, Van Tuan; Hasegawa, Yoshihiko;
Open Access
  • Published: 18 Sep 2019 Journal: Physical Review E, volume 100 (issn: 2470-0045, eissn: 2470-0053, Copyright policy)
  • Publisher: American Physical Society (APS)
Abstract
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing a general framework using a method based on topological data analysis. By considering the diffusion process at a single specified timescale in a network, we map the network nodes to a finite set of points that contains the topological information of the network at a single scale. Subsequently, we study the shape of these point sets over variable timescales that provide scale-variant topological information, to understand the ...
Subjects
free text keywords: Computer Science - Social and Information Networks, Mathematics - Algebraic Topology, Physics - Physics and Society
77 references, page 1 of 6

1. Taylor, D. et al. Topological data analysis of contagion maps for examining spreading processes on networks. Nat. Commun. 6, 7723 (2015).

2. Zan˜udo, J. G. T., Yang, G. & Albert, R. Structure-based control of complex networks with nonlinear dynamics. Proc. Natl Acad. Sci. USA 114, 7234-7239 (2017).

3. Santolini, M. & Baraba´si, A.-L. Predicting perturbation patterns from the topology of biological networks. Proc. Natl Acad. Sci. USA 115, E6375-E6383 (2018). [OpenAIRE]

4. Sun, K., Gonc¸alves, J. P., Larminie, C. & Prˇzulj, N. Predicting disease associations via biological network analysis. BMC Bioinformatics 15, 304 (2014).

5. Calderone, A. et al. Comparing alzheimer's and parkinson's diseases networks using graph communities structure. BMC Syst. Biol. 10, 25 (2016).

6. Schieber, T. A. et al. Quantification of network structural dissimilarities. Nat. Commun. 8, 13928 (2017). [OpenAIRE]

7. Carpi, L., Saco, P., Rosso, O. & Ravetti, M. Structural evolution of the tropical pacific climate network. Eur. Phys. J. B 85, 389 (2012). [OpenAIRE]

8. Barnett, I. & Onnela, J.-P. Change point detection in correlation networks. Sci. Rep. 6, 18893 (2016).

9. Bao, W. & Michailidis, G. Core community structure recovery and phase transition detection in temporally evolving networks. Sci. Rep. 8, 12938 (2018).

10. Ahn, Y.-Y., Bagrow, J. P. & Lehmann, S. Link communities reveal multiscale complexity in networks. Nature 466, 761 (2010).

11. Betzel, R. F. & Bassett, D. S. Multi-scale brain networks. Neuroimage 160, 73-83 (2017).

12. Boulos, R. E., Tremblay, N., Arneodo, A., Borgnat, P. & Audit, B. Multi-scale structural community organisation of the human genome. BMC Bioinformatics 18, 209 (2017). [OpenAIRE]

13. Costa, L. d. F., Rodrigues, F. A., Travieso, G. & Villas Boas, P. R. Characterization of complex networks: A survey of measurements. Adv. Phys. 56, 167-242 (2007).

14. Newman, M. E. J. Networks: An Introduction (Oxford Univ. Press, 2010).

15. Arenas, A., D´ıaz-Guilera, A. & P´erez-Vicente, C. J. Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006).

77 references, page 1 of 6
Abstract
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing a general framework using a method based on topological data analysis. By considering the diffusion process at a single specified timescale in a network, we map the network nodes to a finite set of points that contains the topological information of the network at a single scale. Subsequently, we study the shape of these point sets over variable timescales that provide scale-variant topological information, to understand the ...
Subjects
free text keywords: Computer Science - Social and Information Networks, Mathematics - Algebraic Topology, Physics - Physics and Society
77 references, page 1 of 6

1. Taylor, D. et al. Topological data analysis of contagion maps for examining spreading processes on networks. Nat. Commun. 6, 7723 (2015).

2. Zan˜udo, J. G. T., Yang, G. & Albert, R. Structure-based control of complex networks with nonlinear dynamics. Proc. Natl Acad. Sci. USA 114, 7234-7239 (2017).

3. Santolini, M. & Baraba´si, A.-L. Predicting perturbation patterns from the topology of biological networks. Proc. Natl Acad. Sci. USA 115, E6375-E6383 (2018). [OpenAIRE]

4. Sun, K., Gonc¸alves, J. P., Larminie, C. & Prˇzulj, N. Predicting disease associations via biological network analysis. BMC Bioinformatics 15, 304 (2014).

5. Calderone, A. et al. Comparing alzheimer's and parkinson's diseases networks using graph communities structure. BMC Syst. Biol. 10, 25 (2016).

6. Schieber, T. A. et al. Quantification of network structural dissimilarities. Nat. Commun. 8, 13928 (2017). [OpenAIRE]

7. Carpi, L., Saco, P., Rosso, O. & Ravetti, M. Structural evolution of the tropical pacific climate network. Eur. Phys. J. B 85, 389 (2012). [OpenAIRE]

8. Barnett, I. & Onnela, J.-P. Change point detection in correlation networks. Sci. Rep. 6, 18893 (2016).

9. Bao, W. & Michailidis, G. Core community structure recovery and phase transition detection in temporally evolving networks. Sci. Rep. 8, 12938 (2018).

10. Ahn, Y.-Y., Bagrow, J. P. & Lehmann, S. Link communities reveal multiscale complexity in networks. Nature 466, 761 (2010).

11. Betzel, R. F. & Bassett, D. S. Multi-scale brain networks. Neuroimage 160, 73-83 (2017).

12. Boulos, R. E., Tremblay, N., Arneodo, A., Borgnat, P. & Audit, B. Multi-scale structural community organisation of the human genome. BMC Bioinformatics 18, 209 (2017). [OpenAIRE]

13. Costa, L. d. F., Rodrigues, F. A., Travieso, G. & Villas Boas, P. R. Characterization of complex networks: A survey of measurements. Adv. Phys. 56, 167-242 (2007).

14. Newman, M. E. J. Networks: An Introduction (Oxford Univ. Press, 2010).

15. Arenas, A., D´ıaz-Guilera, A. & P´erez-Vicente, C. J. Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006).

77 references, page 1 of 6
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue