A network with 10 stations offers 45 different journey opportunities ... with 20 stations, that rises to 435 opportunities.
I presume you're referring to Bristol network rather than general opportunities but could you explain the maths here, please? Preferably using nothing more complicated than arithmetic, if possible!
With 1 stations on a system ... Just a pleasure ride
With 2 stations on a system ... 1 flow
With 3 stations on a system ... 1 + 2 = 3 flows
With 4 stations on a system ... 1 + 2 + 3 = 6 flows
With 5 stations on a system ... 1 + 2 + 3 + 4 = 10 flows
etc
Let's look at inner Bristol
Aztec West
and ...
Bristol Parkway
Patchway
Yate
Stapleton Road
Lawrence Hill
Temple Meads
Parson Street
Bedminster
Montpelier
Redland => 55 (11 stations on system)
--------------------------
and ... more general Bristol area
Clifton Down
Sea Mills
Shirehampton
Avonmouth
Nailsea
St Andrews Road
Severn Beach => 153 (18 stations on system)
--------------------------
and ... with some suggested new lines / services stations
Pilning
Coalpit Heath
Portway Parkway
St Annes
Horfield
Ashley Hill
Portishead
Pill
Ashton Gate
Hallen
Henfield
North Filton
Charlton
Long Ashton
Flax Bourton
Thornbury => 561 (34 stations on system)
Volume on flows likely to be very low where stations are close together, increase as distance increases, then decrease again as distance gets even longer.