# Visual Analytics Course

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glossary_definitions_notations

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 — glossary_definitions_notations [2016/05/07 21:47] (current)melancon created 2016/05/07 21:47 melancon created 2016/05/07 21:47 melancon created Line 1: Line 1: + ===== Visual Analytics Course ===== + ==== Glossary, Notations, Definitions ==== + + **Graph** A //graph// is denoted as $G = (V, E)$ with //nodes// or //vertices $V$, and //edges// $E$. + + **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//​. + + Unless otherwise stated, definitions apply to either directed or undirected graphs (with slight modifications). + + **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 + + $$N_G(u) = \{ v \in V \ | \ (u, v) \in E\}$$ + + or $N(u)$ for sake of simplicity. + + **Path** A //path// is a sequence of edges that shares endpoints + + $$e_0 = (u_0, v_0), e_1 = (U_1, v_1), \ldots, e_k = (u_k, v_k)$$ + + with $v_0 = u_1$, $v_1 = u_2, \ldots, v_{k-1} = u_k$. + + **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. +