Search results
Results from the WOW.Com Content Network
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. [1] [2] The theory of random graphs lies at the intersection between graph theory and probability theory.
Exponential Random Graph Models (ERGMs) are a family of statistical models for analyzing data from social and other networks. [1] [2] Examples of networks examined using ERGM include knowledge networks, [3] organizational networks, [4] colleague networks, [5] social media networks, networks of scientific development, [6] and others.
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.
A certain category of small-world networks were identified as a class of random graphs by Duncan Watts and Steven Strogatz in 1998. [4] They noted that graphs could be classified according to two independent structural features, namely the clustering coefficient, and average node-to-node distance (also known as average shortest path length).
In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups.For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.
In network science, the Configuration Model is a family of random graph models designed to generate networks from a given degree sequence. Unlike simpler models such as the Erdős–Rényi model , Configuration Models preserve the degree of each vertex as a pre-defined property.
An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level. To randomize the runs, one way would be to put 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having level 3.
It is known that a wide variety of abstract graphs exhibit the small-world property, e.g., random graphs and scale-free networks. Further, real world networks such as the World Wide Web and the metabolic network also exhibit this property. In the scientific literature on networks, there is some ambiguity associated with the term "small world".