Search results
Results from the WOW.Com Content Network
Depending on the context the graph can be directed or undirected. A state x v for each vertex v of Y taken from a finite set K. The system state is the n-tuple x = (x 1, x 2, ... , x n), and x[v] is the tuple consisting of the states associated to the vertices in the 1-neighborhood of v in Y (in some fixed order). A vertex function f v for each ...
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in their article published in 1998 in the Nature scientific journal. [ 1 ]
In spectral clustering and graph-based signal processing, where graph vertices represent data points, the edge weights can be computed, e.g., as inversely proportional to the distances between pairs of data points, leading to all weights being non-negative with larger values informally corresponding to more similar pairs of data points. Using ...
The function Φ(t,x) is called the evolution function of the dynamical system: it associates to every point x in the set X a unique image, depending on the variable t, called the evolution parameter. X is called phase space or state space, while the variable x represents an initial state of the system. We often write
A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point [1] [2] and exactly one inflection point. Properties
It allows the translation of various partial differential equations, e.g., the heat equation, to the graph setting. Based on the first-order partial difference operators on graphs one can formally derive a family of weighted graph -Laplace operators,: () for < by minimization of the discrete -Dirichlet energy functional
Force-directed graph drawing algorithms assign forces among the set of edges and the set of nodes of a graph drawing.Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs ...
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.