The heat kernel as the pagerank of a graph

By Fan Chung. Proceedings of the National Academy of Sciences of the United States of America, 2007

294 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/03df1f721201e09e3286acd439bb00dc17c9e279

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In Computational Theory and Mathematics

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Citations in the corpus

Algorithms for Detecting Significantly Mutated Pathways in Cancer (2010, unknown): “Note that this diffusion process is related to the diffusion kernel (Kondor and Lafferty, 2002) or heat kernel (Chung, 2007), which models the diffusion of heat on a graph, and these diffusion processes are in turn related to certain random walks on graphs (Doyle and Snell, 1984; Lova´sz, 1993).”
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters (2008, methodology): “We will also extensively use Local Spectral Algorithm of Andersen, Chung, and Lang [13] to find node sets of low conductance, i.e., good communities, around a seed node.”
Random walks and diffusion on networks (2016, unknown): “is defined for strongly connected networks) [308, 309].”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Finally, there is a rich history connecting random walks on graphs to connectivity and near zeroth-order homology, often formalized through ideas from spectral graph theory such as the discrete Cheeger inequality and isoperimetric inequality [4, 36,78, 83,88,116].”
Statistical properties of community structure in large social and information networks (2008, methodology): “Similar results were originally proven by Spielman and Teng [147, 148], who analyzed local random walks on a graph; see Chung [34, 36, 35] for an exposition of the relationship between these methods.”
Diffusion Improves Graph Learning (2019, background): “PPR corresponds to choosing T = Trw and θPPR k = α(1 − α), with teleport probability α ∈ (0, 1) [14].”
Handbook of Big Data (2016, background): “• The PageRank diffusion [16] • The Katz diffusion [42] • The heat kernel diffusion [29,43] • The truncated random walk diffusion [44]”
Learning Structural Node Embeddings via Diffusion Wavelets (2017, methodology): “Another line of related work are graph diffusion kernels [5] which have been utilized for various graph modeling purposes [3, 22, 29, 34].”
Learning Graphs From Data: A Signal Representation Perspective (2018, background): “Particularly, the graph diffusion model can be widely applied in real-world scenarios to understand the distribution of heat (sources) [43], such as the propagation of a heat wave in geographical spaces, the movement of people in buildings or vehicles in cities, and the shift of people’s interest to”
Pan-Cancer Network Analysis Identifies Combinations of Rare Somatic Mutations across Pathways and Protein Complexes (2014, unknown): “This pattern of mutations complicates the identification of recurrent mutations in individual genes, and indeed only half of the genes in the complex (STAG2, SMC1A, and RAD21) were significant by at least one of the three gene scores.”