We could have done with an explanation of what the fields of your structure actually represent.
Assuming that the field A is the adjacency matrix of your graph (you really should have told us that), then:
matcontent = load('dolphins.mat');
network = graph(matcontent.Problem.A, cellstr(matcontent.Problem.aux.nodename));
plot(network);
See the documentation of graph.plot for the various plotting options as the default plot is quite messy. In particular, you may want to play with the 'Layout' option.
edit: fixed typo in nodename
