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In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a specified probability distribution) and connecting two nodes by a link if and only if their distance is in a given range, e.g. smaller than a certain neighborhood radius, r.
Network science. 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.
In 1961, Gilbert introduced the random plane network [13] (more commonly referred to now as a random geometric graph (RGG), or Gilbert Disk model) where points are placed on the infinite plane using a suitable Point Process and nodes connect if and only if they are within some critical connection range R; wireless communication networks were ...
There are two closely related variants of the Erdős–Rényi random graph model. A graph generated by the binomial model of Erdős and Rényi (p = 0.01) In the (,) model, a graph is chosen uniformly at random from the collection of all graphs which have nodes and edges. The nodes are considered to be labeled, meaning that graphs obtained from ...
Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is related to the visual representation of such rotation within the human mind. [1] There is a relationship between areas of the brain associated with perception and mental rotation.
Network neuroscience is an approach to understanding the structure and function of the human brain through an approach of network science, through the paradigm of graph theory. [1] A network is a connection of many brain regions that interact with each other to give rise to a particular function. [2] Network Neuroscience is a broad field that ...
As a physical system with graph-like properties, [6] a large-scale brain network has both nodes and edges and cannot be identified simply by the co-activation of brain areas. In recent decades, the analysis of brain networks was made feasible by advances in imaging techniques as well as new tools from graph theory and dynamical systems.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P (k) of nodes in the network having k connections to other nodes goes for large values of k as. where is a parameter whose value is typically in the range (wherein the second moment (scale parameter) of is infinite ...