What does the "share a line segment with" selection method require?

The correct choice highlights that the "share a line segment with" selection method requires at least two contiguous vertices in common between the features. This means that for two line segments to be considered sharing a segment, they must physically connect at two points along their paths, effectively forming a continuous line. This method is particularly useful in various GIS applications where maintaining spatial relationships and connectivity is essential for analysis, such as in transportation networks or hydrological modeling.

In this context, the requirement for contiguous vertices implies that the features must not only meet at a point but also extend alongside each other for a certain length, thus forming a true segment connection. This criterion ensures that the selected features are genuinely linked in a meaningful spatial manner, allowing for accurate spatial analysis and representation in the GIS.

The other options do not adequately capture the necessary physical relationship between the features. For instance, having only one point in common might not constitute a true shared segment, and shared edges without common vertices would not represent a connected segment in the intended sense. Moreover, the idea of features being completely within each other pertains to containment rather than sharing line segments, which does not align with the requirements outlined in the selection method.