networks

neighboring vertices found along incoming edges


Calling Sequence


arrivals (v, G);
arrivals (G)


Parameters


v



vertex or set of vertices of G

G



graph or network





Description


•

Given a vertex v of a graph G, this routine returns the set of vertices which are at the tail of edges directed into v or at the end of an undirected edge incident with v. Thus, undirected edges are treated as if they were bidirectional.

•

If v is a set of vertices then arrival is defined in terms of arrival into the subgraph induced by v in G.

•

When called with just the graph as a single argument, an arrivals table indexed by vertices is constructed. This table is not part of the graph data structure. In particular, this means that any direct assignments to this table have no effect on the graph itself.

•

The arrivals and departure information is constructed from the neighbors table which is automatically maintained by the main graph primitives such as addedge() and delete().

•

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[arrivals](...).



Examples


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

$\mathrm{with}\left(\mathrm{networks}\right)\:$

>

$G\u2254\mathrm{complete}\left(4\right)\:$

>

$\mathrm{addvertex}\left(0\,G\right)$

>

$\mathrm{connect}\left(0\,1\,G\,\mathrm{directed}\right)$

>

$\mathrm{arrivals}\left(0\,G\right)$

>

$\mathrm{departures}\left(0\,G\right)$

>

$\mathrm{neighbors}\left(0\,G\right)$

>

$\mathrm{arrivals}\left(1\,G\right)$

$\left\{{0}{\,}{2}{\,}{3}{\,}{4}\right\}$
 (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) 
>

$\mathrm{arrivals}\left(G\right)$

${\mathrm{table}}\left(\left[{0}{\=}\left\{{}\right\}{\,}{1}{\=}\left\{{0}{\,}{2}{\,}{3}{\,}{4}\right\}{\,}{2}{\=}\left\{{1}{\,}{3}{\,}{4}\right\}{\,}{3}{\=}\left\{{1}{\,}{2}{\,}{4}\right\}{\,}{4}{\=}\left\{{1}{\,}{2}{\,}{3}\right\}\right]\right)$
 (9) 
>

$\mathrm{departures}\left(G\right)$

${\mathrm{table}}\left(\left[{0}{\=}\left\{{1}\right\}{\,}{1}{\=}\left\{{2}{\,}{3}{\,}{4}\right\}{\,}{2}{\=}\left\{{1}{\,}{3}{\,}{4}\right\}{\,}{3}{\=}\left\{{1}{\,}{2}{\,}{4}\right\}{\,}{4}{\=}\left\{{1}{\,}{2}{\,}{3}\right\}\right]\right)$
 (10) 
>

$\mathrm{neighbors}\left(G\right)$

${\mathrm{table}}\left(\left[{0}{\=}\left\{{1}\right\}{\,}{1}{\=}\left\{{0}{\,}{2}{\,}{3}{\,}{4}\right\}{\,}{2}{\=}\left\{{1}{\,}{3}{\,}{4}\right\}{\,}{3}{\=}\left\{{1}{\,}{2}{\,}{4}\right\}{\,}{4}{\=}\left\{{1}{\,}{2}{\,}{3}\right\}\right]\right)$
 (11) 






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