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Note that if you remove the "biifinite", there is no problem, because of the empty path. Usually, when we speak about "components", we expect to get a partition of the ground set, your definition breaks that. I do understand the behaviour you expect, but imho, it should be at most an option, definitely not the default, the default should be what is expected from an average graph theorist.

Note that if you remove the "biifinite", "binifinite", there is no problem, because of the empty path. Usually, when we speak about "components", we expect to get a partition of the ground set, your definition breaks that. I do understand the behaviour you expect, but imho, it should be at most an option, definitely not the default, the default should be what is expected from by an average graph theorist.

Note that if you remove the "binifinite", "biinfinite", there is no problem, because of the empty path. Usually, when we speak about "components", we expect to get a partition of the ground set, your definition breaks that. I do understand the behaviour you expect, but imho, it should be at most an option, definitely not the default, the default should be what is expected by an average graph theorist.