"Informally, a graph is a finite set of dots called vertices (or nodes) connected by links called edges (or arcs). More formally: a simple graph is a (usually finite) set of vertices V and set of unordered pairs of distinct elements of V called edges." (Craig F Smith & H Peter Alesso, "Thinking on the Web: Berners-Lee, Gödel and Turing", 2008)
"A computation object that is used to model relationships among things. A graph is defined by two finite sets: a set of nodes and a set of edges. Each node has a label to identify it and distinguish it from other nodes. Edges in a graph connect exactly two nodes and are denoted by the pair of labels of nodes that are related." (Clay Breshears, "The Art of Concurrency", 2009)
"A graph in mathematics is a set of nodes and a set of edges between pairs of those nodes; the edges are ordered or nonordered pairs, or a relation, that defines the pairs of nodes for which the relation being examined is valid. […] The edges can either be undirected or directed; directed edges depict a relation that requires the nodes to be ordered while an undirected edge defines a relation in which no ordering of the edges is implied."
[undirected graph:] "A graph in which the nodes of an edge are unordered. This implies that the edge can be thought of as a two-way path." (Clay Breshears, "The Art of Concurrency", 2009)
[directed graph:] "A graph whose edges are ordered pairs of nodes; this allows connections between nodes in one direction. When drawn, the edges of a directed graph are commonly shown as arrows to indicate the “direction” of the edge." (Clay Breshears, "The Art of Concurrency", 2009)
"1.Generally, a set of homogeneous nodes (vertices) and edges (arcs) between pairs of nodes." (DAMA International, "The DAMA Dictionary of Data Management", 2011)
[directed acyclic graph:] "A graph that defines a partial order so that nodes can be sorted into a linear sequence with references only going in one direction. A directed acyclic graph has, as its name suggests, directed edges and no cycles." (Michael McCool et al, "Structured Parallel Programming", 2012)
"A data structure that consists of a set of nodes and a set of edges that relate the nodes to each other" (Nell Dale & John Lewis, "Computer Science Illuminated" 6th Ed., 2015)
[directed graph:] "A directed graph is one in which the edges have a specified direction from one vertex to another." (Dan Sullivan, "NoSQL for Mere Mortals", 2015)
[directed graph (digraph):] "A graph in which each edge is directed from one vertex to another (or the same) vertex" (Nell Dale & John Lewis, "Computer Science Illuminated" 6th Ed., 2015)
[undirected graph:] "A graph in which the edges have no direction" (Nell Dale & John Lewis, "Computer Science Illuminated" 6th Ed., 2015)
[undirected graph:] "An undirected graph is one in which the edges do not indicate a direction (such as from-to) between two vertices." (Dan Sullivan, "NoSQL for Mere Mortals®", 2015)
"Like a tree, a graph consists of a set of nodes connected by edges. These edges may or may not have a direction. If they do, the graph is referred to as a 'directed graph'. If a graph is directed, it may be possible to start at a node and follow edges in a path that leads back to the starting node. Such a path is called a 'cycle'. If a directed graph has no cycles, it is referred to as an 'acyclic graph'." (Robert J Glushko, "The Discipline of Organizing: Professional Edition" 4th Ed., 2016)
"In a computer science or mathematics context, a graph is a set of nodes and edges that connect the nodes." (Alex Thomas, "Natural Language Processing with Spark NLP", 2020)
Undirected graph "A graph in which the edges have no direction" (Nell Dale et al, "Object-Oriented Data Structures Using Java" 4th Ed., 2016)
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