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glossary_definitions_notations [2016/05/07 21:47] (current)
melancon created
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 +===== 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.
 + 
/net/html/perso/melancon/Visual_Analytics_Course/data/pages/glossary_definitions_notations.txt · Last modified: 2016/05/07 21:47 by melancon