In this study, we revisit the concepts of basis path testing, linearly independent paths and the cyclomatic number where several examples are given to discuss the formal definition. It is then shown that a sequence of paths, where each path introduces at least a new edge that is not present in previous paths, are linearly independent. Building such a sequence where the size is equal to the cyclomatic number ensures that these paths form a basis path set which guides the design of respective test cases. This investigation clarifies several statements made in scholarly published papers which state that every path in a basis path set introduces at least one new (unique) edge that is not present in other paths. This study highlights the need of a more rigorous commentaries when stating the uniqueness of edges in a basis path set and linearly independent paths.