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
- 4.Grady D, Thiemann C, Brockmann D (2011) Parameter-free identification of salient features in complex networks. arXiv:1110.3864
- 8.Bollobás B, Borgs C, Chayes J, Riordan O (2003) Directed scale-free graphs. In: Proceedings of the fourteenth annual ACM-SIAM symposium on discrete algorithms, pp 132–139 Google Scholar