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The partition of a graph into its level structure may be used as a heuristic for graph layout problems such as graph bandwidth. [1] The Cuthill–McKee algorithm is a refinement of this idea, based on an additional sorting step within each level.
A level structure of the graph, given a starting vertex, is a partition of the graph's vertices into subsets by their distances from the starting vertex. A geodetic graph is one for which every pair of vertices has a unique shortest path connecting them.
A multi-level graph partitioning algorithm works by applying one or more stages. Each stage reduces the size of the graph by collapsing vertices and edges, partitions the smaller graph, then maps back and refines this partition of the original graph. [6]
When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x 1, x 2 and x 3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables. A level set is a special case of a fiber.
A Reeb graph [1] (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolution of the level sets of a real-valued function on a manifold. [2] According to [ 3 ] a similar concept was introduced by G.M. Adelson-Velskii and A.S. Kronrod and applied to analysis of Hilbert's thirteenth problem . [ 4 ]
Drain plot : A two-dimensional plot where the data are presented in a hierarchy with multiple levels. The levels are nested in the sense that the pieces in each pie chart add up to 100%. A waterfall or waterdrop metaphor is used to link each layer to the one below visually conveying the hierarchical structure. Drain Plot. [4]
Level The level of a node is the number of edges along the unique path between it and the root node. [4] This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).