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glossary_definitions_notations

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+ | ===== Visual Analytics Course ===== | ||

+ | ==== Glossary, Notations, Definitions ==== | ||

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+ | **Graph** A //graph// is denoted as $G = (V, E)$ with //nodes// or //vertices $V$, and //edges// $E$. | ||

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+ | **Edge** An //edge// is a pair of nodes $u, v \in V$. The pair is ordered $e = (u, v) \in E$ when $G$ is //directed. It is unordered $e = \{u, v\} \in E$ when $G$ is //undirected//. | ||

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+ | Unless otherwise stated, definitions apply to either directed or undirected graphs (with slight modifications). | ||

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+ | **Neighbor** A node $v \in V$ is a //neighbor// of a node $u \in V$ exactly when $(u, v) \in V$, that is when $u$ and $v$ are connected by an edge. The set of neighbors of a node $u \in V$ is denoted as | ||

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+ | $$N_G(u) = \{ v \in V \ | \ (u, v) \in E\}$$ | ||

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+ | or $N(u)$ for sake of simplicity. | ||

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+ | **Path** A //path// is a sequence of edges that shares endpoints | ||

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+ | $$e_0 = (u_0, v_0), e_1 = (U_1, v_1), \ldots, e_k = (u_k, v_k)$$ | ||

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+ | with $v_0 = u_1$, $v_1 = u_2, \ldots, v_{k-1} = u_k$. | ||

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+ | **Cycle / Circuit** When the start and end node of a path coincide, $v_k = u_0$, the path is called a //cycle//. When $G$ is directed, the name //circuit// is sometimes preferred. | ||

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/net/html/perso/melancon/Visual_Analytics_Course/data/pages/glossary_definitions_notations.txt · Last modified: 2016/05/07 21:47 by melancon