Graph view vs. implementation

The relation between implementation variables and the graph abstraction is given by the following relations:

• A bridge portal is the prime portal iff prime is equal to its unique 64-bit identity and alpha is true.
• A bridge represents a directed edge in the net tree iff for both portals, mute is false, and for one of the portals alpha is false or it is the prime portal, and for the other portal alpha is true and it is not the prime portal. The directed bridge is an outgoing edge on the bus where the adjacent portal's alpha is true and it is not the prime portal, and it is an incoming edge on the other bus.
• A bridge represents an undirected edge in the net tree iff for both portals, mute is true and each portal's alpha is false.
• A bridge represents a directed edge in the bus tree for bus id $b$ iff it is a directed edge in the net tree, and route map[$b$] is forward for one portal, and valid for the other portal. The directed bridge is an outgoing edge on the bus with the forward entry, and it is an incoming edge on the other bus.
• A bridge represents an undirected edge in the bus tree for bus id $b$ iff it is a undirected edge in the net tree, and route map[$b$] is valid for both portals.
• A bridge does not represent an edge in the bus tree for bus id $b$ iff for both portals, route map[$b$] is clean or dirty. The value dirty represents a bus id for which the bus tree is being destroyed, it is a temporary value that only occurs during net update.

Any bridge state that is not covered by the above possibilities is an inconsistent state and cannot occur in the net update protocol, except the `half-directed' edge in a bus tree, where route map[$b$] is valid for one portal and dirty for its co-portal. This is treated as an incoming edge as well on the bus with the valid entry.