In Ahlfor's Complex Analysis 3rd edition, page 138, chapter 3.4.1, it's stated that:

A chain is [called] a cycle if it can be represented as a sum of closed curves. Very simple combinatorical considerations show that a chain is a cycle if and only if in any representation the initial and end points of the individual arcs are identical in pairs. Thus it is immediately possible to tell whether a chain is a cycle or not.

I am not exactly sure what the above is saying. I know the definition of a chain (of arcs in complex plane) and a closed curve, yet the last two sentences of the above eludes me. A specific example for clarification would be great.


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