Zeta Functions of Finite Graphs

By M. Kotani, T. Sunada. 2000

244 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/414ee80c27c5c9272ca35907fa1be1cf843513d4

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Citations in the corpus

THE NON-BACKTRACKING SPECTRUM OF THE UNIVERSAL COVER OF A GRAPH (2007, methodology): “Theorem 3.3 (Bass [Bas92], Kotani and Sunada [ KS00 ]).”
Riemann–Roch and Abel–Jacobi theory on a finite graph (2006, background): “Let d :C0(G,R) → C1(G,R) and d∗ :C1(G,R) → C0(G,R) be the usual operators on cochains (see [1, §1]).”
Non-backtracking random walks and a weighted Ihara's theorem (2016, methodology): “This difference from [10] is one of the primary difficulties in generalizing this result.”
Probability on Trees and Networks (2017, result): “(d)–(h) Similar results can be found in Kotani and Sunada (2000) and for non-regular graphs in Angel, Friedman, and Hoory (2007). For (h) with G infinite, use the fact that κ ∈ σ(B) iff κ̄ is an eigenvalue of B∗ or κ is an approximate eigenvalue of B (i.”
Spectral radii of sparse random matrices (2017, background): “[19]) implies a simple relation between the spectrum of the adjacency matrix and the nonbacktracking matrix.”
Nonbacktracking spectrum of random graphs: Community detection and nonregular Ramanujan graphs (2018, background): “where ζG is the Ihara zeta function of the graph; refer to [16, 19, 29, 30].”
Heat kernels on regular graphs and generalized Ihara zeta function formulas (2013, unknown): “In a special case, we recover the standard formula stemming from Ihara’s work [17], which in turn is generalized in [2,12,15,20,33] for finite graphs; see Subsect.”
A new proof of Friedman's second eigenvalue theorem and its extension to random lifts (2015, unknown): “The Ihara-Bass formula asserts that if G ∈ Gd(n) and r = |E|/2 − |V | = nd/2− n, det(IE −Bz) = (1− z(2)) det(IV −Az + (d− 1)z(2)IV ), (5) for a proof, we refer to [14, 25].”
Cutoff on all Ramanujan graphs (2015, background): “that appear implicitly in [20] (see also [5,7,8] as well as [26, Exercise 6.”