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networks

 departures
 neighboring vertices found along outgoing edges

 Calling Sequence departures(v, G) departures(G)

Parameters

 v - vertex of G G - graph or network

Description

 • Important: The networks package has been deprecated.  Use the superseding command GraphTheory[Departures] instead.
 • Given a vertex v of a graph G, this routine returns the set of vertices which are at the head of edges directed out of v.
 • Undirected edges are treated as if they were bidirectional.
 • The arrivals and departure information is constructed from the neighbors table which is automatically maintained by the graph primitives such as addedge() and delete().
 • When no vertices are specified a departures table, indexed by vertices, is constructed. This table is not part of the graph data structure so that the graph remains unaffected by assignments to the table.
 • This routine is normally loaded using the command with(networks) but may also be referenced using the full name networks[departures](...).

Examples

Important: The networks package has been deprecated.  Use the superseding command GraphTheory[Departures] instead.

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{addvertex}\left(0,G\right)$
 ${0}$ (1)
 > $\mathrm{connect}\left(0,1,G,\mathrm{directed}\right)$
 ${\mathrm{e7}}$ (2)
 > $\mathrm{arrivals}\left(0,G\right)$
 ${\varnothing }$ (3)
 > $\mathrm{departures}\left(0,G\right)$
 $\left\{{1}\right\}$ (4)
 > $\mathrm{neighbors}\left(0,G\right)$
 $\left\{{1}\right\}$ (5)
 > $\mathrm{arrivals}\left(1,G\right)$
 $\left\{{0}{,}{2}{,}{3}{,}{4}\right\}$ (6)
 > $\mathrm{departures}\left(1,G\right)$
 $\left\{{2}{,}{3}{,}{4}\right\}$ (7)
 > $\mathrm{neighbors}\left(1,G\right)$
 $\left\{{0}{,}{2}{,}{3}{,}{4}\right\}$ (8)
 > $\mathrm{arrivals}\left(G\right)$
 ${table}{}\left(\left[{0}{=}{\varnothing }{,}{1}{=}\left\{{0}{,}{2}{,}{3}{,}{4}\right\}{,}{2}{=}\left\{{1}{,}{3}{,}{4}\right\}{,}{3}{=}\left\{{1}{,}{2}{,}{4}\right\}{,}{4}{=}\left\{{1}{,}{2}{,}{3}\right\}\right]\right)$ (9)
 > $\mathrm{departures}\left(G\right)$
 ${table}{}\left(\left[{0}{=}\left\{{1}\right\}{,}{1}{=}\left\{{2}{,}{3}{,}{4}\right\}{,}{2}{=}\left\{{1}{,}{3}{,}{4}\right\}{,}{3}{=}\left\{{1}{,}{2}{,}{4}\right\}{,}{4}{=}\left\{{1}{,}{2}{,}{3}\right\}\right]\right)$ (10)
 > $\mathrm{neighbors}\left(G\right)$
 ${table}{}\left(\left[{0}{=}\left\{{1}\right\}{,}{1}{=}\left\{{0}{,}{2}{,}{3}{,}{4}\right\}{,}{2}{=}\left\{{1}{,}{3}{,}{4}\right\}{,}{3}{=}\left\{{1}{,}{2}{,}{4}\right\}{,}{4}{=}\left\{{1}{,}{2}{,}{3}\right\}\right]\right)$ (11)