Heat diffusion: thermodynamic depth complexity of networks
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Title: | Heat diffusion: thermodynamic depth complexity of networks |
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Authors: | Escolano, Francisco | Hancock, Edwin R. | Lozano, Miguel Angel |
Research Group/s: | Laboratorio de Investigación en Visión Móvil (MVRLab) |
Center, Department or Service: | Universidad de Alicante. Departamento de Ciencia de la Computación e Inteligencia Artificial |
Keywords: | Diffusion kernel | Decomposition | Graph complexity | Polytopal measure | Thermodynamic depth |
Knowledge Area: | Ciencia de la Computación e Inteligencia Artificial |
Issue Date: | 14-Mar-2012 |
Publisher: | American Physical Society |
Citation: | Phys. Rev. E 85, 036206 (2012) [15 pages]. doi:10.1103/PhysRevE.85.036206 |
Abstract: | In this paper we use the Birkhoff–von Neumann decomposition of the diffusion kernel to compute a polytopal measure of graph complexity. We decompose the diffusion kernel into a series of weighted Birkhoff combinations and compute the entropy associated with the weighting proportions (polytopal complexity). The maximum entropy Birkhoff combination can be expressed in terms of matrix permanents. This allows us to introduce a phase-transition principle that links our definition of polytopal complexity to the heat flowing through the network at a given diffusion time. The result is an efficiently computed complexity measure, which we refer to as flow complexity. Moreover, the flow complexity measure allows us to analyze graphs and networks in terms of the thermodynamic depth. We compare our method with three alternative methods described in the literature (Estrada's heterogeneity index, the Laplacian energy, and the von Neumann entropy). Our study is based on 217 protein-protein interaction (PPI) networks including histidine kinases from several species of bacteria. We find a correlation between structural complexity and phylogeny (more evolved species have statistically more complex PPIs). Although our methods outperform the alternatives, we find similarities with Estrada's heterogeneity index in terms of network size independence and predictive power. |
Sponsor: | F.E. and M.L. are funded by Project No. TIN2008-04416 of the Spanish Government. E.R.H. is funded by the EU FET Project SIMBAD and a Royal Society Wolfson Research Merit Award. |
URI: | http://hdl.handle.net/10045/35865 |
ISSN: | 1539-3755 (Print) | 1550-2376 (Online) |
DOI: | 10.1103/PhysRevE.85.036206 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | ©2012 American Physical Society |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1103/PhysRevE.85.036206 |
Appears in Collections: | INV - MVRLab - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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2012_Escolano_etal_PhysRevE.pdf | 1,07 MB | Adobe PDF | Open Preview | |
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