The following figure illustrates the railway network in Switzerland. France Lausanne, Geneva Neuchtel 3 Bem Basel 11 Olten Zermatt Interlaken 10 Visp Lucerne 9 6 Zrich Switzerland 8 Lugano Chur Germany Austria Italy 1. Can a passenger go from any station to any other? What is the name for this property? (1p) Next write the unweighted adjacency matrix A of this railway network (note that stations have already been assigned a node number) and relying upon A and its powers answer the following: 2. Is the graph acyclic? Is it periodic? If yes, what is the period? (1p) (1p) 3. What is the number of links on the shortest path connecting Geneva and Zurich? 4. Is it possible to go from Zermatt to Chur in 5 links? What about 10 links? (1p) 5. How many different routes with strictly less than 7 links and possibly visiting the same hub more than once start from Interlaken and end in Basel? (1p)