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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 ...
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]
Graphs with trillions of edges occur in machine learning, social network analysis, and other areas. Compressed graph representations have been developed to reduce I/O and memory requirements. General techniques such as Huffman coding are applicable, but the adjacency list or adjacency matrix can be processed in specific ways to increase ...
Neighbourhoods may be used to represent graphs in computer algorithms, via the adjacency list and adjacency matrix representations. Neighbourhoods are also used in the clustering coefficient of a graph, which is a measure of the average density of its neighbourhoods. In addition, many important classes of graphs may be defined by properties of ...
1 Examples and types of graphs. 2 Graph coloring. ... This is a list of graph theory topics, ... Adjacency list; Adjacency matrix.
list 1. An adjacency list is a computer representation of graphs for use in graph algorithms. 2. List coloring is a variation of graph coloring in which each vertex has a list of available colors. local A local property of a graph is a property that is determined only by the neighbourhoods of the vertices in the graph. For instance, a graph is ...
A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1]. The first example of cospectral graphs was reported by Collatz and ...
For, the adjacency matrix of a directed graph with n vertices can be any (0,1) matrix of size , which can then be reinterpreted as the adjacency matrix of a bipartite graph with n vertices on each side of its bipartition. [27] In this construction, the bipartite graph is the bipartite double cover of the directed graph.