Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also

is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in HE we characterize the Friedrichs extension of the HE-graph Laplacian. We consider infinite connected network-graphs G = (V,E), V for vertices, and E for edges. To every

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling

Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties

Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same character-istics are determined

Abstract. This paper uses chain complexes of based, finitely-generated Z-modules to study the Laplacians of signed plane graphs. We extend a theorem of Lien and Watkins [6] regarding the Goeritz equivalence of the signed Laplacians of a signed plane graph and its dual by showing that it is possible

Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals

the dependence structure through a graph Laplacian matrix. We also generalize the graph Laplacian to allow both positively and negatively correlated variables. A prior distribution for the graph Laplacian is then proposed, which allows conjugacy and thereby greatly simplifies the computation. We show

eigenvalues

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