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Alternatively, If A is an adjacency matrix for the graph, modified to have nonzero entries on its main diagonal, then the nonzero entries of A k give the adjacency matrix of the k th power of the graph, [14] from which it follows that constructing k th powers may be performed in an amount of time that is within a logarithmic factor of the time ...
In computational biology, power graph analysis is a method for the analysis and representation of complex networks. Power graph analysis is the computation, analysis and visual representation of a power graph from a graph . Power graph analysis can be thought of as a lossless compression algorithm for graphs. [1]
That is, G is an induced subgraph of the graph power , induced by the leaves of T. For a graph G constructed in this way, T is called a k-leaf root of G. A graph is a leaf power if it is a k-leaf power for some k. [1] These graphs have applications in phylogeny, the problem of reconstructing evolutionary trees.
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
In algebraic number theory the n-th power residue symbol (for an integer n > 2) is a generalization of the (quadratic) Legendre symbol to n-th powers. These symbols are used in the statement and proof of cubic , quartic , Eisenstein , and related higher [ 1 ] reciprocity laws .
(For a graph with n vertices and r terminals, they use t = n − r − 1 added vertices per tree.) Then, they ask for the k -minimum spanning tree in this augmented graph with k = rt . The only way to include this many vertices in a k -spanning tree is to use at least one vertex from each added tree, for there are not enough vertices remaining ...
Three weeks after President Donald Trump's inauguration, the federal judiciary is beginning to rein in the president's unilateral efforts to reshape the federal government. On Saturday, a federal ...
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions.It is a data transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association (such as the Pearson correlation between variables), and for other data stabilization procedures.