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This undirected cyclic graph can be described by the three unordered lists {b, c}, {a, c}, {a, b}. In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph.
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Because of its lack of standardization, the format has many variations. [1] For instance, some implementations of the format require the node IDs to be integers, [3] while others allow more general alphanumeric identifiers. Each node definition is a single line of text starting with the node ID, separated by a space from its label.
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.
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]
A parallel for the adjacency matrix of a hypergraph can be drawn from the adjacency matrix of a graph. In the case of a graph, the adjacency matrix is a square matrix which indicates whether pairs of vertices are adjacent.
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 ...
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.