Silinq

A name with possibilities.

A route is a sequence of allowed arrows

The supplied graph has four nodes, A, B, C and D, and exactly four directed links: A to B, B to C, A to D and D to C. There are no other links. A route may follow an arrow only in its indicated direction. The task is to identify direct neighbours and reachable destinations, counting a link traversal as one step. The worksheet counts destinations reached by at least one step, so a starting node is not included merely because the route begins there.

Silinq.com
Four directed edges in the Silinq directed-route worksheetExactly four directed linksABDCA → B · B → C · A → D · D → C

01

List direct neighbours before tracing longer routes

From A, the direct outgoing neighbours are B and D. C is not a direct neighbour because there is no arrow from A to C. From B, the only outgoing neighbour is C, and from D it is also C. C has no outgoing neighbours in the supplied graph. Write these four adjacency lists before tracing routes: A lists B and D; B lists C; D lists C; C lists none. This separates the actual edges from connections that may become possible by following more than one edge in sequence.

Two routes to one destination in the Silinq directed-route worksheetA → B → CA → D → CTwo routes · one destination CShortest A-to-C route: 2 stepsFrom A, distinct destinations: B, D, C

02

Count destinations separately from the routes that reach them

Starting at A, B and D are reachable in one step. C is reachable in two steps through either A to B to C or A to D to C. There are therefore three distinct reachable destinations from A, even though C has two different routes leading to it. The shortest route from A to C has two steps. This exercise treats every edge as one step; it assigns no time, cost or capacity to any edge. Equal step counts do not establish that two real-world routes would take equal time or perform equally well.

The reverse route is absent in the Silinq directed-route worksheetC has no outgoing edgesNo route from C to AA route is not automatically reversibleNew edges require a revised worksheetFollow arrow direction at every step

03

Check the reverse question against the actual arrows

Starting at C, none of A, B or D is reachable because C has no outgoing edges. The existence of a route from A to C does not create a reverse route from C to A. A reusable worksheet records the node list, directed edge list, start node, direct neighbours, reachable destinations and one explicit route for each claimed destination. If a new arrow from C to A is added, create a revised edge list before recalculating. That change creates cycles and alters reachability, so conclusions from the original four-edge graph should not be carried forward without review.

silinq.com

Explore Silinq

Held for potential development. Acquisition inquiries may be considered.

Domain inquiry ↗