Geometric multiplicity of unitary non-backtracking eigenvalues

Published 4 May 2022 in math.CO | (2205.02004v1)

Abstract: We completely characterize the conditions under which a complex unitary number is an eigenvalue of the non-backtracking matrix of an undirected graph. Further, we provide a closed formula to compute its geometric multiplicity and describe an algorithm to compute this multiplicity without making a single matrix computation. The algorithm has time complexity that is linear in the size of the graph.

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Leo Torres

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