Random Walks on Simplicial Complexes and the Normalized Hodge 1-Laplacian
From MaRDI portal
Publication:5113166
DOI10.1137/18M1201019zbMath1441.05205arXiv1807.05044OpenAlexW3099736351MaRDI QIDQ5113166
Michael T. Schaub, Ali Jadbabaie, Austin R. Benson, Gabor Lippner, Paul S. Horn
Publication date: 3 June 2020
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.05044
random walksnetworksHodge decompositionsimplicial complexesdiffusion processesHodge Laplacianspectral embeddingPageRank
Social networks; opinion dynamics (91D30) Applications of graph theory (05C90) Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Graph theory (including graph drawing) in computer science (68R10) Data structures (68P05) Simplicial sets and complexes in algebraic topology (55U10) Combinatorial aspects of simplicial complexes (05E45) Random walks on graphs (05C81)
Related Items
Networks beyond pairwise interactions: structure and dynamics, Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs, Random Simplicial Complexes: Models and Phenomena, Flow-Based Community Detection in Hypergraphs, Signal Processing on Simplicial Complexes, What Are Higher-Order Networks?, The structure and dynamics of networks with higher order interactions, Quantifying the structural stability of simplicial homology, A general higher-order supracentrality framework based on motifs of temporal networks and multiplex networks, Dynamical analysis of Hyper-SIR rumor spreading model, Hodge Laplacians on Graphs, Toward a spectral theory of cellular sheaves, Political structures and the topology of simplicial complexes, Opinion dynamics with multi-body interactions, Consensus on simplicial complexes: Results on stability and synchronization
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Cheeger-type inequality on simplicial complexes
- On eigenvalues of random complexes
- Statistical ranking and combinatorial Hodge theory
- \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
- Main-memory triangle computations for very large (sparse (power-law)) graphs
- Approximate counting, uniform generation and rapidly mixing Markov chains
- The nonlinear statistics of high-contrast patches in natural images
- Random walks and diffusion on networks
- Centralities in simplicial complexes. Applications to protein interaction networks
- Isoperimetric inequalities in simplicial complexes
- Complex networks: structure and dynamics
- Spectra of combinatorial Laplace operators on simplicial complexes
- Coverage in sensor networks via persistent homology
- Diffusion maps
- Stability analysis of diagonally equipotent matrices
- A new status index derived from sociometric analysis
- Harmonic functions and boundary value problems on a chain complex
- PageRank Beyond the Web
- Random walks on simplicial complexes and harmonics
- Clique topology reveals intrinsic geometric structure in neural correlations
- Simplicial complexes: Spectrum, homology and random walks
- Why do simple algorithms for triangle enumeration work in the real world?
- Statistical mechanics of complex networks
- Dualities in persistent (co)homology
- LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
- Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
- AN APPLICATION OF ALGEBRAIC TOPOLOGY TO NUMERICAL ANALYSIS: ON THE EXISTENCE OF A SOLUTION TO THE NETWORK PROBLEM
- Statistical Methods in Markov Chains
- Topology of random simplicial complexes: a survey
- Discrete Calculus
- Testing contractibility in planar rips complexes
- Topology and data
- Arboricity and Subgraph Listing Algorithms
- LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
- Algebraic Potential Theory on Graphs
- The Structure and Function of Complex Networks
- Spectral Properties of Hypergraph Laplacian and Approximation Algorithms
- A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data
- Fastest Mixing Markov Chain on a Graph
- Deeper Inside PageRank
- COBOUNDARY EXPANDERS
- Distributed Coverage Verification in Sensor Networks Without Location Information
- Simplicial Models and Topological Inference in Biological Systems
- Axioms for Centrality
- $P$-persistent homology of finite topological spaces
- Spectral sparsification of simplicial complexes for clustering and label propagation
- Hodge Laplacians on Graphs
- Topology of viral evolution
- A Unifying Perron--Frobenius Theorem for Nonnegative Tensors via Multihomogeneous Maps
- Exploring complex networks
- Tensor Analysis
- Solving 1-Laplacians in Nearly Linear Time: Collapsing and Expanding a Topological Ball
- Lx = b
- Barcodes: The persistent topology of data
- Networks
