Abstract
We consider Cheeger Inequalities for general edge-weighted directed graphs. Previously the directed case was considered by Chung for a probability transition matrix corresponding to a strongly connected graph with weights induced by a stationary distribution. An Eulerian property of these special weights reduces these instances to the undirected case, for which recent results on multi-way spectral partitioning and higher-order Cheeger Inequalities can be applied.
We extend Chung’s approach to general directed graphs. In particular, we obtain higher-order Cheeger Inequalities for the following scenarios:
(1) The underlying graph needs not be strongly connected.
(2) The weights can deviate (slightly) from a stationary distribution.
This research is partially funded by a grant from Hong Kong RGC under the contract HKU17200214E.
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Chan, TH.H., Tang, Z.G., Zhang, C. (2015). Cheeger Inequalities for General Edge-Weighted Directed Graphs. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_3
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DOI: https://doi.org/10.1007/978-3-319-21398-9_3
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