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  2. Signed graph - Wikipedia

    en.wikipedia.org/wiki/Signed_graph

    A signed graph is the special kind of gain graph in which the gain group has order 2. The pair (G, B(Σ)) determined by a signed graph Σ is a special kind of biased graph. The sign group has the special property, not shared by larger gain groups, that the edge signs are determined up to switching by the set B(Σ) of balanced cycles. [19]

  3. Shoe size - Wikipedia

    en.wikipedia.org/wiki/Shoe_size

    Typically, this will be the shortest length deemed practical; but this can be different for children's, teenagers', men's, and women's shoes - making it difficult to compare sizes. In America, the baseline for women's shoes is seven inches and for men's it is 7 ⁠ 1 / 3 ⁠ in.; in the UK, the baseline for both is 7 ⁠ 2 / 3 ⁠ in. [2]

  4. Spectral graph theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_graph_theory

    A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1]. The first example of cospectral graphs was reported by Collatz and ...

  5. Laplacian matrix - Wikipedia

    en.wikipedia.org/wiki/Laplacian_matrix

    Spectral graph theory relates properties of a graph to a spectrum, i.e., eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. Imbalanced weights may undesirably affect the matrix spectrum, leading to the need of normalization — a column/row scaling of the matrix entries ...

  6. Trace diagram - Wikipedia

    en.wikipedia.org/wiki/Trace_diagram

    By definition, a trace diagram's function is computed using signed graph coloring. For each edge coloring of the graph's edges by n labels, so that no two edges adjacent to the same vertex have the same label, one assigns a weight based on the labels at the vertices and the labels adjacent to the matrix labels. These weights become the ...

  7. Spectral shape analysis - Wikipedia

    en.wikipedia.org/wiki/Spectral_shape_analysis

    Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc.

  8. Spectral geometry - Wikipedia

    en.wikipedia.org/wiki/Spectral_geometry

    Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. The case of the Laplace–Beltrami operator on a closed Riemannian manifold has been most intensively studied, although other Laplace operators in differential geometry ...

  9. Spectrum (physical sciences) - Wikipedia

    en.wikipedia.org/wiki/Spectrum_(physical_sciences)

    Discrete spectra are seen in many other phenomena, such as vibrating strings, microwaves in a metal cavity, sound waves in a pulsating star, and resonances in high-energy particle physics. The general phenomenon of discrete spectra in physical systems can be mathematically modeled with tools of functional analysis , specifically by the ...

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