| Full text | |
| Author(s): |
Ye, Cheng
;
Comin, Cesar H.
;
Peron, Thomas K. D. M.
;
Silva, Filipi N.
;
Rodrigues, Francisco A.
;
Costa, Luciano da F.
;
Torsello, Andrea
;
Hancock, Edwin R.
Total Authors: 8
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 92, n. 3, p. 16-pg., 2015-09-25. |
| Abstract | |
In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution. (AU) | |
| FAPESP's process: | 13/26416-9 - Modelling of dynamical processes in complex networks |
| Grantee: | Francisco Aparecido Rodrigues |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/50986-7 - Graph spectra and complex network evolution |
| Grantee: | Luciano da Fontoura Costa |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 11/22639-8 - Unveiling the relationship between structure and dynamics on modular networks |
| Grantee: | Cesar Henrique Comin |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 11/50761-2 - Models and methods of e-Science for life and agricultural sciences |
| Grantee: | Roberto Marcondes Cesar Junior |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/50761-2 - Models and methods of e-Science for life and agricultural sciences |
| Grantee: | Roberto Marcondes Cesar Junior |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/22160-7 - Synchronization of Kuramoto Oscillators in Complex Networks |
| Grantee: | Thomas Kaue Dal Maso Peron |
| Support Opportunities: | Scholarships in Brazil - Doctorate |