View source for Graph (graph theory)

:: '''Not to be confused with: ''[[Digraph]]'''''
{{Provisional page|grade=B|msg=Unsure of whether or not 2 edges from the same node "to" the same node are allowed, and if so how they'd be distinct, eg 2 pipes of weight 5 are feasible between 2 nodes. Or even one node!}}
__TOC__{{Infobox|title=Graph|above=(Discrete mathematics)|image=[[File:DiscreteMathsGraphPicture.png|thumb|A typical graph]]}}
==Definition==
: {{Caveat|Here we describe a finite graph;}} infinite graphs are a thing, but they require special handling<ref group="Note">See Topology from Saul in 2015, I never found a source but he used trees!</ref>
A ''graph'' is defined to be an [[ordered pair]] {{M|(V,E)}}<ref>That formal languages hardback by my bed, sort it out later, DUBIOUS REFERENCE for graph, great for digraph</ref> where:
* {{M|V}} be a [[finite set]] whose elements we shall call ''vertices'' (singular: ''vertex'') or ''nodes'' (singular: ''node'')
* {{M|E}} is a finite set of ''edges'' (singular: ''edge''), which may or may not have data associated with them:
** '''No data: ''' - An edge is defined as an [[unordered pair|(unordered) pair]], {{M|\{v_1,v_2\} }} of vertices {{M|v_1,v_2\in V}}, which need not be distinct (note that then {{M|\{v,v\} }} is the [[singleton]] {{M|\{v\} }}, which represents an edge from {{M|v}} to itself)
** '''Data: ''' - An edge is defined as the [[ordered pair]], {{M|(\{v_i,v_j\},d_{i,j})}} of an [[unordered pair]] {{M|\{v_i,v_j\} }} specifying the edge as above and for some associated data, {{M|d_{i,j} }}
{{Warning|Multiple edges between the same vertices is not allowed in this model}}, yet having 2 edges 'from' a vertex 'to' itself both of weight 5 is allowed without problem in "real" graphs, indicating a limitation of our definition
==Terminology==
{{Requires work|grade=B|msg=Standard graph terminology}}
==Notes==
<references group="Note"/>
==References==
<references/>
{{CS Definition|Discrete Mathematics|Graph Theory}}