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An introduction to grids, graphs, and networks / Constantine Pozrikidis
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Oxford ; New York : Oxford University Press, [2014]Description: Online-Ressource (xii, 284 pages)ISBN:- 1306426626
- 9780199996735
- 9781306426626
- 511.5
- QA166
Contents:
Summary: A concise introduction to graphs and networks, presenting theoretical concepts at a level accessible to both professionals and students.Summary: Cover -- CONTENTS -- PREFACE -- ONE-DIMENSIONAL GRIDS -- 1.1 POISSON EQUATION IN ONE DIMENSION -- 1.2 DIRICHLET BOUNDARY CONDITION AT BOTH ENDS -- 1.3 NEUMANN-DIRICHLET BOUNDARY CONDITIONS -- 1.4 DIRICHLET-NEUMANN BOUNDARY CONDITIONS -- 1.5 NEUMANN BOUNDARY CONDITIONS -- 1.6 PERIODIC BOUNDARY CONDITIONS -- 1.7 ONE-DIMENSIONAL GRAPHS -- 1.7.1 Graph Laplacian -- 1.7.2 Adjacency Matrix -- 1.7.3 Connectivity Lists and Oriented Incidence Matrix -- 1.8 PERIODIC ONE-DIMENSIONAL GRAPHS -- 1.8.1 Periodic Adjacency Matrix -- 1.8.2 Periodic Oriented Incidence Matrix -- 1.8.3 Fourier Expansions -- 1.8.4 Cosine Fourier Expansion -- 1.8.5 Sine Fourier Expansion -- GRAPHS AND NETWORKS -- 2.1 ELEMENTS OF GRAPH THEORY -- 2.1.1 Adjacency Matrix -- 2.1.2 Node Degrees -- 2.1.3 The Complete Graph -- 2.1.4 Complement of a Graph -- 2.1.5 Connectivity Lists and the Oriented Incidence Matrix -- 2.1.6 Connected and Unconnected Graphs -- 2.1.7 Pairwise Distance and Diameter -- 2.1.8 Trees -- 2.1.9 Random and Real-Life Networks -- 2.2 LAPLACIAN MATRIX -- 2.2.1 Properties of the Laplacian Matrix -- 2.2.2 Complete Graph -- 2.2.3 Estimates of Eigenvalues -- 2.2.4 Spanning Trees -- 2.2.5 Spectral Expansion -- 2.2.6 Spectral Partitioning -- 2.2.7 Complement of a Graph -- 2.2.8 Normalized Laplacian -- 2.2.9 Graph Breakup -- 2.3 CUBIC NETWORK -- 2.4 FABRICATED NETWORKS -- 2.4.1 Finite-Element Network on a Disk -- 2.4.2 Finite-Element Network on a Square -- 2.4.3 Delaunay Triangulation of an Arbitrary Set of Nodes -- 2.4.4 Delaunay Triangulation of a Perturbed Cartesian Grid -- 2.4.5 Finite Element Network Descending from an Octahedron -- 2.4.6 Finite Element Network Descending from an Icosahedron -- 2.5 LINK REMOVAL AND ADDITION -- 2.5.1 Single and Multiple Link -- 2.5.2 Link Addition -- 2.6 INFINITE LATTICES -- 2.6.1 Bravais Lattices -- 2.6.2 Archimedean Lattices.PPN: PPN: 807407968Package identifier: Produktsigel: ZDB-26-MYL | ZDB-38-EBR | ZDB-30-PAD | ZDB-30-PQE
Cover; CONTENTS; PREFACE; ONE-DIMENSIONAL GRIDS; 1.1 POISSON EQUATION IN ONE DIMENSION; 1.2 DIRICHLET BOUNDARY CONDITION AT BOTH ENDS; 1.3 NEUMANN-DIRICHLET BOUNDARY CONDITIONS; 1.4 DIRICHLET-NEUMANN BOUNDARY CONDITIONS; 1.5 NEUMANN BOUNDARY CONDITIONS; 1.6 PERIODIC BOUNDARY CONDITIONS; 1.7 ONE-DIMENSIONAL GRAPHS; 1.7.1 Graph Laplacian; 1.7.2 Adjacency Matrix; 1.7.3 Connectivity Lists and Oriented Incidence Matrix; 1.8 PERIODIC ONE-DIMENSIONAL GRAPHS; 1.8.1 Periodic Adjacency Matrix; 1.8.2 Periodic Oriented Incidence Matrix; 1.8.3 Fourier Expansions; 1.8.4 Cosine Fourier Expansion
1.8.5 Sine Fourier ExpansionGRAPHS AND NETWORKS; 2.1 ELEMENTS OF GRAPH THEORY; 2.1.1 Adjacency Matrix; 2.1.2 Node Degrees; 2.1.3 The Complete Graph; 2.1.4 Complement of a Graph; 2.1.5 Connectivity Lists and the Oriented Incidence Matrix; 2.1.6 Connected and Unconnected Graphs; 2.1.7 Pairwise Distance and Diameter; 2.1.8 Trees; 2.1.9 Random and Real-Life Networks; 2.2 LAPLACIAN MATRIX; 2.2.1 Properties of the Laplacian Matrix; 2.2.2 Complete Graph; 2.2.3 Estimates of Eigenvalues; 2.2.4 Spanning Trees; 2.2.5 Spectral Expansion; 2.2.6 Spectral Partitioning; 2.2.7 Complement of a Graph
2.2.8 Normalized Laplacian2.2.9 Graph Breakup; 2.3 CUBIC NETWORK; 2.4 FABRICATED NETWORKS; 2.4.1 Finite-Element Network on a Disk; 2.4.2 Finite-Element Network on a Square; 2.4.3 Delaunay Triangulation of an Arbitrary Set of Nodes; 2.4.4 Delaunay Triangulation of a Perturbed Cartesian Grid; 2.4.5 Finite Element Network Descending from an Octahedron; 2.4.6 Finite Element Network Descending from an Icosahedron; 2.5 LINK REMOVAL AND ADDITION; 2.5.1 Single and Multiple Link; 2.5.2 Link Addition; 2.6 INFINITE LATTICES; 2.6.1 Bravais Lattices; 2.6.2 Archimedean Lattices; 2.6.3 Laves Lattices
2.6.4 Other Two-Dimensional Lattices2.6.5 Cubic Lattices; 2.7 PERCOLATION THRESHOLDS; 2.7.1 Link (Bond) Percolation Threshold; 2.7.2 Node Percolation Threshold; 2.7.3 Computation of Percolation Thresholds; SPECTRA OF LATTICES; 3.1 SQUARE LATTICE; 3.1.1 Isolated Network; 3.1.2 Periodic Strip; 3.1.3 Doubly Periodic Network; 3.1.4 Doubly Periodic Sheared Network; 3.2 MÖBIUS STRIPS; 3.2.1 Horizontal Strip; 3.2.2 Vertical Strip; 3.2.3 Klein Bottle; 3.3 HEXAGONAL LATTICE; 3.3.1 Isolated Network; 3.3.2 Doubly Periodic Network; 3.3.3 Alternative Node Indexing; 3.4 MODIFIED UNION JACK LATTICE
3.4.1 Isolated Network3.4.2 Doubly Periodic Network; 3.5 HONEYCOMB LATTICE; 3.5.1 Isolated Network; 3.5.2 Brick Representation; 3.5.3 Doubly Periodic Network; 3.5.4 Alternative Node Indexing; 3.6 KAGOMÉ LATTICE; 3.6.1 Isolated Network; 3.6.2 Doubly Periodic Network; 3.7 SIMPLE CUBIC LATTICE; 3.8 BODY-CENTERED CUBIC (BCC) LATTICE; 3.9 FACE-CENTERED CUBIC (FCC) LATTICE; NETWORK TRANSPORT; 4.1 TRANSPORT LAWS AND CONVENTIONS; 4.1.1 Isolated and Embedded Networks; 4.1.2 Nodal Sources; 4.1.3 Linear Transport; 4.1.4 Nonlinear Transport; 4.2 UNIFORM CONDUCTANCES; 4.2.1 Isolated Networks
4.2.2 Embedded Networks
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