Mathematics of networks
By Mark Newman. Oxford Scholarship Online, 2018
417 citations recorded by the source corpus.
An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/dce4848f314d1bc4eae80ea5efd1390654a4c341
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In Computational Theory and Mathematics
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Robust Malware Detection for Internet of (Battlefield) Things Devices Using Deep Eigenspace Learning (2019, background): “this condition, there should be an explicit eigengap in the matrix’s eigenvalues [35], and Fig.”
- Graph Representation Learning (2020, methodology): “we require positive centrality values, we can apply the Perron-Frobenius Theorem(1) to further determine that the vector of centrality values e is given by the eigenvector corresponding to the largest eigenvalue of A [Newman, 2016].”