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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.
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.
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 edges.
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.
For example, there is a k(n) (approximately equal to 2log 2 (n)) such that the largest clique in G(n, 0.5) has almost surely either size k(n) or k(n) + 1. [7] Thus, even though finding the size of the largest clique in a graph is NP-complete, the size of the largest clique in a "typical" graph (according to this model) is very well understood.
In the Robinson–Schensted correspondence between permutations and Young tableaux, the length of the first row of the tableau corresponding to a permutation equals the length of the longest increasing subsequence of the permutation, and the length of the first column equals the length of the longest decreasing subsequence. [3]
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.