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A network is not traversable if there are three or more nodes that are connected by an odd number of edges (odd nodes). This is because any network with three or more odd nodes inadvertently creates nodes that are accessible either through one or two edges, and usually, these nodes get more and more isolated each time an edge of the graph is traversed until it cannot be reached anymore. However, a network with one or two odd nodes does not create isolated points and can therefore still mean that the network is traversable.

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