Algebraic graph theory

square matrix used to represent a graph or network

matrix that shows the relationship between two classes of objects

matrix representation of a graph

graph representing faces of another graph

number defined from a node-link network quantifying how likely it is that two neighbors of a randomly chosen node will be adjacent

theorem of computing the number of spanning trees in a graph

the study of the properties of a graph in relationship to matrices associated with the graph

In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin. Over time, the concept has expanded substantially, leading to the development of hundreds of distin

type of matrix in algebraic graph theory

branch of mathematics in which algebraic methods are applied to problems about graphs

type of graph which admit an automorphism on adjacent vertices

graph in which the number of shared neighbors of two vertices depends only on whether they are adjacent

clustering methods

symmetry of a graph onto itself preserving the edge–vertex connectivity

graph whose automorphism group acts transitively upon its vertices

graph where any two nodes of equal distance are isomorphic

Matrix in math with special properties

graph that is edge-transitive and regular but not vertex-transitive

spectral graph theory concept

node-link graph for which all eigenvalues of its characteristic polynomial are integers

graph whose automorphism group acts transitively upon its edges

special case of a strongly regular graph

measure of network community structure

sum of the absolute values of the eigenvalues of the adjacency matrix

a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k

second-smallest eigenvalue of a graph Laplacian

graph that is both vertex-transitive and edge-transitive, but not symmetric

theorem