What are the pros and cons for using either a linklist, a linkmap or an edge to store relationships between my vertices ?
An edge defines a relationship between two vertices. For example, you define two vertices, Person and Car. You then define an Edge Drives. This edge ties the two vertices together. "Jane" Drives "Ford".
A linklist is a list of classes associated with another class. A Car class might have a linklist of parts from the Part class. A car consists of multiple parts.
A linkmap is a map of key, class values associate with another class. A car class might have a linkmap of PartType, Part. A car consists of multiple parts, which can be grouped by engine, body, chassis, etc.