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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 ...
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.
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 ...
The edge (,) is called the inverted edge of (,). Multiple edges , not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [ 5 ] a directed graph is an ordered triple G = ( V , E , ϕ ) {\displaystyle G=(V,E,\phi )} comprising:
In general, the parallel edge processing based on 2D partitioning can be organized in 2 communication phases, which are "expand" phase and "fold" phase. [ 6 ] In the "expand" phase, if the edge list for a given vertex is the column of the adjacency matrix, then for each vertex v in the frontier, the owner of v is responsible to tell other ...
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
A GraphML file consists of an XML file containing a graph element, within which is an unordered sequence of node and edge elements. Each node element should have a distinct id attribute, and each edge element has source and target attributes that identify the endpoints of an edge by having the same value as the id attributes of those endpoints.
Graph (discrete mathematics), a structure made of vertices and edges Graph theory, the study of such graphs and their properties; Graph (topology), a topological space resembling a graph in the sense of discrete mathematics