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# Graphs two

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### Graphs two

1. 1. Boris, Ben, Bob, Bess, Beth and Bill are waiting in adoctor’s surgery. Looking around the room, each of themsees that they know some of the other people in the room.Ben knows five of the other people sitting in the room,Bob knows four of the others,Beth and Bill both know three of the others,Bess knows two of the others andBoris only knows one of the other people.Who knows who in the waiting room?
2. 2. Adjacency Matrices• Directed and Undirected Graphs• Weighted graphs
3. 3. Adjacency Matrix or List• Matrix is fast and direct• Quick for adding and deleting edges• Not so good for adding and deleting vertices• Can be very ‘sparse’ and therefore inefficient
4. 4. Paths and Path problems• From one vertex to another along edges• Explorer’s problem• Path that travels each edge once and returns to starting point• Traveller’s problem• Path that visits each vertex only once before returning to starting point.
5. 5. Closed paths and cycles• Closed Path or circuit: Path that ends at the starting vertex• Cycle circuit for which each intermediate vertex is different• Tree Undirected connected graph with no cycles
6. 6. Closed paths and cycles• Closed Path or circuit: Path that ends at the starting vertex• Cycle circuit for which each intermediate vertex is different• Tree Undirected connected graph with no cycles