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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.
If the edge has a label, it appears on the same line after the endpoint IDs. [3] The graph may be interpreted as a directed or undirected graph. For directed graphs, to specify the concept of bi-directionality in an edge, one may either specify two edges (forward and back) or differentiate the edge by means of a label.
List structures include the edge list, an array of pairs of vertices, and the adjacency list, which separately lists the neighbors of each vertex: Much like the edge list, each vertex has a list of which vertices it is adjacent to.
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 ...
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
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
where the degree of a vertex counts the number of times an edge terminates at that vertex. In an undirected graph , this means that each loop increases the degree of a vertex by two. In a directed graph , the term degree may refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at ...