$4 \cdot 61$ Given that in the subway network, each line has at least 4 stations, of which no more than 3 are transfer stations, and at each transfer station, no more than two lines intersect. If from any station, one can reach any other station with at most two transfers, how many lines can this network have at most?
［Solution］Fix one line, on which there are at most 3 stations available for transfer, so from this line, one can transfer to at most 3 other lines. And from each of these 3 lines, one can transfer to at most 2 new lines. Therefore, the total number of lines is no more than $1+3+3 \times 2=10$.

On the other hand, the network of lines shown in the right figure has 10 lines and meets all the requirements of the problem. Therefore, the maximum number of lines is 10.