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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 ...
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A graph that is locally H is claw-free if and only if the independence number of H is at most two; for instance, the graph of the regular icosahedron is claw-free because it is locally C 5 and C 5 has independence number two. The locally linear graphs are the graphs in which every neighbourhood is an induced matching. [5]
The minimum rank of a graph is always at most equal to n − 1, where n is the number of vertices in the graph. [1] For every induced subgraph H of a given graph G, the minimum rank of H is at most equal to the minimum rank of G. [2] If a graph is disconnected, then its minimum rank is the sum of the minimum ranks of its connected components. [3]
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 ...
For each vertex we store the list of adjacencies (out-edges) in order of the planarity of the graph (for example, clockwise with respect to the graph's embedding). We then initialize a counter = + and begin a Depth-First Traversal from . During this traversal, the adjacency list of each vertex is visited from left-to-right as needed.
This simple model is commonly known as the adjacency list model and was introduced by Dr. Edgar F. Codd after initial criticisms surfaced that the relational model could not model hierarchical data. [citation needed] However, the model is only a special case of a general adjacency list for a graph.
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.
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