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An edge list is a data structure used to represent a graph as a list of its edges. An (unweighted) edge is defined by its start and end vertex, so each edge may be represented by two numbers. [1] The entire edge list may be represented as a two-column matrix. [2] [3] An edge list may be considered a variation on an adjacency list which is ...
An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
Adjacency lists are generally preferred for the representation of sparse graphs, while an adjacency matrix is preferred if the graph is dense; that is, the number of edges | | is close to the number of vertices squared, | |, or if one must be able to quickly look up if there is an edge connecting two vertices.
is the adjacency matrix of the observed network, with = if there is an edge between and , and = otherwise. k i k j 2 L {\displaystyle {\frac {k_{i}k_{j}}{2L}}} represents the expected probability of an edge between nodes i {\displaystyle i} and j {\displaystyle j} under the configuration model.
The adjacency matrix may be used as a data structure for the representation of graphs in computer programs for manipulating graphs. The main alternative data structure, also in use for this application, is the adjacency list. [11] [12]
The nested set model is a solution to that problem. An alternative solution is the expression of the hierarchy as a parent-child relation. Joe Celko called this the adjacency list model. If the hierarchy can have arbitrary depth, the adjacency list model does not allow the expression of operations such as comparing the contents of hierarchies ...
A hypergraph homomorphism is a map from the vertex set of one hypergraph to another such that each edge maps to one other edge. A hypergraph H = ( X , E ) {\displaystyle H=(X,E)} is isomorphic to a hypergraph G = ( Y , F ) {\displaystyle G=(Y,F)} , written as H ≃ G {\displaystyle H\simeq G} if there exists a bijection
Global approaches rely on properties of the entire graph and do not rely on an arbitrary initial partition. The most common example is spectral partitioning, where a partition is derived from approximate eigenvectors of the adjacency matrix, or spectral clustering that groups graph vertices using the eigendecomposition of the graph Laplacian ...