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If the question state:
A connected and undirected graph, then does this graph allow loop or multiple edges?

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I searched over the internet, but some allow, some don't. It's so confusing. Any idea? Thank you.

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It depends on the source. –  Qiaochu Yuan Sep 9 '11 at 4:37
    
@Qiaochu Yuan: Thank you. So if the question does not explicitly state so, then loop are not allowed right? –  Chan Sep 9 '11 at 4:44
    
@Chan: probably. –  anon Sep 9 '11 at 5:05
    
You should check not the question, but the beginning of the text (probably where the term "graph" is first defined). Authors tend to say something like, "Unless otherwise stated, 'graph' means 'simple graph'". –  Austin Mohr Sep 9 '11 at 5:53
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1 Answer 1

up vote 3 down vote accepted

Most of the results that are covered in a graph theory course concern "simple" graphs, that in general do not permit self-loof or multiple edges. Graphs that allow multiple edges between two vertices are known as multi-graphs. Graphs that permit self-loops are sometimes called pseudo-graphs.

The restriction on multiple edges between two vertices is sometimes weakened for directed graphs so that both $(a,b)$ and $(b,a)$ can be included in the edge set of the directed graph.

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Many thanks, I got the idea. –  Chan Sep 9 '11 at 5:22
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