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The utilization of graph theory in neuroscience studies has been actively applied after the discovery of functional brain networks. In graph theory, an N × N adjacency matrix (also called a connection matrix) with the elements of zero or non-zero indicates the absence or presence of a relationship between the vertices of a network with N nodes.
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
It is thus identical to the question of the node connectivity of a given graph in discrete mathematics. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally sized group with a network in which every pair of persons has at least this number of separate paths between them.
A graph with connectivity 4. In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected.
In mathematics, computer science and network science, network theory is a part of graph theory.It defines networks as graphs where the vertices or edges possess attributes. . Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) compone
A subfield of connectomics deals with the comparison of the brain graphs of multiple subjects. It is possible to build a consensus graph such the Budapest Reference Connectome by allowing only edges that are present in at least connectomes, for a selectable parameter. The Budapest Reference Connectome has led the researchers to the discovery of ...
Connectomics is the production and study of connectomes: comprehensive maps of connections within an organism's nervous system.More generally, it can be thought of as the study of neuronal wiring diagrams with a focus on how structural connectivity, individual synapses, cellular morphology, and cellular ultrastructure contribute to the make up of a network.
A directed graph or digraph is a graph in which edges have ... especially in the study of Erdős and Rényi of the asymptotic probability of graph connectivity, ...