CycFlowDec: A Python module for decomposing flow networks using simple cycles

New algorithms for determining the expected flow through simple cycles in a closed network are presented. Current network analysis software do not implement algorithms for expected cyclic flow decomposition, despite its potential value. Decomposing networks into expected cycle flows provides a quantitative characterization of network cycles that can be further analyzed for sensitivity and correlative behavior. An efficient, general algorithm has been coded into CycFlowDec, an open source Python module available at https://github.com/austenb28/CycFlowDec.

[1]  Steve Horvath,et al.  WGCNA: an R package for weighted correlation network analysis , 2008, BMC Bioinformatics.

[2]  Gregory A. Voth,et al.  The Origin of Coupled Chloride and Proton Transport in a Cl–/H+ Antiporter , 2016, bioRxiv.

[3]  Dalibor Froncek,et al.  Cyclic decompositions of complete graphs into spanning trees , 2004, Discuss. Math. Graph Theory.

[4]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek: Revised and Expanded Edition for Updated Software , 2018 .

[5]  Loni Hagen,et al.  Crisis Communications in the Age of Social Media , 2018 .

[6]  Sterling Thomas,et al.  A survey of current software for network analysis in molecular biology , 2010, Human Genomics.

[7]  Jörn Dunkel,et al.  Stochastic cycle selection in active flow networks , 2016, Proceedings of the National Academy of Sciences.

[8]  Marc Timme,et al.  Cycle flows and multistability in oscillatory networks. , 2016, Chaos.

[9]  Rui Ding,et al.  Detecting the urban traffic network structure dynamics through the growth and analysis of multi-layer networks , 2018, Physica A: Statistical Mechanics and its Applications.

[10]  Qian Minping,et al.  Circulation for recurrent markov chains , 1982 .

[11]  R. Banisch,et al.  Reactive flows and unproductive cycles for random walks on complex networks , 2015 .

[12]  Xiaofei Wang,et al.  Understanding characteristics in multivariate traffic flow time series from complex network structure , 2017 .

[13]  Mudita Singhal,et al.  COPASI - a COmplex PAthway SImulator , 2006, Bioinform..

[14]  Martina Morris,et al.  statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data. , 2008, Journal of statistical software.

[15]  GENERIC QUANTUM MARKOV SEMIGROUPS, CYCLE DECOMPOSITION AND DEVIATION FROM EQUILIBRIUM , 2012 .

[16]  D. R. Fulkerson,et al.  On the Max Flow Min Cut Theorem of Networks. , 1955 .

[17]  Christof Schütte,et al.  Cycle-flow–based module detection in directed recurrence networks , 2014, ArXiv.

[18]  Geoffrey S. Cook,et al.  Striped Mullet Migration Patterns in the Indian River Lagoon: A Network Analysis Approach to Spatial Fisheries Management , 2020, Marine and Coastal Fisheries.

[19]  Zenghui Wang,et al.  Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review , 2017, Neural Computation.

[20]  M. Qian,et al.  Cycle symmetries and circulation fluctuations for discrete-time and continuous-time Markov chains , 2014, 1407.1263.

[21]  S. Kalpazidou.  Cycle representations of Markov processes , 1995 .

[22]  R. Simha,et al.  Process-based network decomposition reveals backbone motif structure , 2010, Proceedings of the National Academy of Sciences.

[23]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[24]  Leandros Tassiulas,et al.  Cyclic motifs in the Sardex monetary network , 2018, Nature Human Behaviour.

[25]  Jessica M J Swanson,et al.  Multiscale Simulations Reveal Key Aspects of the Proton Transport Mechanism in the ClC-ec1 Antiporter. , 2016, Biophysical journal.