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All these models had one thing in common: they all predicted very short average path length. [1] The average path length depends on the system size but does not change drastically with it. Small world network theory predicts that the average path length changes proportionally to log n, where n is the number of nodes in the network.
Watts–Strogatz small-world model generated by igraph and visualized by Cytoscape 2.5. 100 nodes. 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.
Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy.
Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. (animated version)In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
Given an initial path, TPS provides some algorithms to perturb that path and create a new one. As in all Monte Carlo walks, the new path will then be accepted or rejected in order to have the correct path probability. The procedure is iterated and the ensemble is gradually sampled. A powerful and efficient algorithm is the so-called shooting ...
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices ; the length of a path may either be measured by its number of edges, or (in weighted graphs ) by the sum of the weights of its ...
Viterbi path and Viterbi algorithm have become standard terms for the application of dynamic programming algorithms to maximization problems involving probabilities. [3] For example, in statistical parsing a dynamic programming algorithm can be used to discover the single most likely context-free derivation (parse) of a string, which is ...
Seidel's algorithm is an algorithm designed by Raimund Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. [1] It solves the problem in () expected time for a graph with vertices, where < is the exponent in the complexity () of matrix multiplication.