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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.
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.
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 principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, [1] can be considered as a generalization of the principle of maximum entropy. It postulates that the most unbiased probability distribution of paths is the one that maximizes their Shannon entropy. This entropy of paths is sometimes called ...
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.
Then the number ,, is the probability that a random walk of length k starting at v ends at w. In particular, if G is a graph with root 0 , p 0 , 0 , 2 k {\displaystyle p_{0,0,2k}} is the probability that a 2 k {\displaystyle 2k} -step random walk returns to 0 .
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.
Kleiber's law: for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the animal's mass. Named after Max Kleiber. Kluge's law: a sound law that purports to explain the origin of the Proto-Germanic long consonants. Named after Friedrich Kluge. Koomey's law: the energy of computation is halved every year and a half.