Decimation of Fast States and Weak Nodes: Topological Variation via Persistent Homology
We study the topological variation in Markov processes and networks due to a coarse-graining procedure able to preserve the Markovian property. Such coarse-graining method simplifies master equation by neglecting the fast states and significantly reduces the network size by decimating weak nodes.
We use persistent homology to identify the robust topological structure which survive after the coarse-graining.
KeywordsMarkov processes Complex networks Coarse-graining (theory) Persistent homology Computational topology
L. Rondoni gratefully acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement No. 202680. The EC is not liable for any use that can be made on the information contained herein.
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