41 burrow systems of the fossorial form of the water vole (Arvicola terrestris L.), a small rodent inhabiting meadows, pastures and orchards in central Europe, have been analysed using methods of graph theory. Four main types exist : a) linear structures (trees), b) trees with a few cycles, c) mixture of linear and cyclic structures, d) essentially cyclic structures. The intersections with 3 branches clearly predominate (97 %). The lengths of the edges (segments joining a dead-end and an intersection or two intersections) follow an exponential distribution with a mean and a standard deviation being usually very close. The nest is generally closer to a central point than would be expected by chance. The connections between any two intersections or an intersection and a dead-end can be summarised in the form of an adjacency matrix ; a method of reducing its size by eliminating the trees connected to the cyclic part was used when computing the shortest paths, in order to save computing time and space. Two simulation models are briefly described. The first one is rather simple and produces planar graphs with straight edges. The second one is more elaborate, has more parameters and approximates real burrow systems quite well ; it also allows to take into account areas of favourable and unfavourable environment and the behaviour of voles accordingly.
