Network Types: Minimal Networks

This post will discuss Minimal Transit Networks, for other network types see an Overview of Network Types. For route types see an Overview of Route Type Geometry.

Minimal Network

This is the most simple type of network and consists of one route (R=1) that connects all serviced stations. Every station (N) is connected to two others by a route segment (RS) or one other station if it is the start-point or final destination of a non-circular route. This type of network is the travelling salesman problem.

RS = N   or   RS = N-1   and   R=1

If a municipality or a entrepreneurial company were to start a public transportation service this type of network will in most cases be the one chosen. It is the logical beginning of a public transportation network. The advantages lie within it’s simplicity and capacity utilization. Only a small amount of vehicles are necessary to provide (rudimentary) services to an area. The disadvantages are that it is slow and prone to delays and disruption. Depending if the focus is on coverage or rider-ship a circular, maeander, or direct route can be chosen.

Apart from a villages or towns, obvious candidates for a Minimal Transit Network are university campuses, large spread out hospitals, large factories, fairgrounds, pensioner communities or holiday resorts. An efficient transit system can be of great benefit and reduce time and cost necessary to maintain individual transportation modes (cars, walking or cycling).

Circular Minimal Network


A Circular Minimal Network consists of a route that services all points-of-interest with stations, driving from one to the next around in a circle. By closing the route the circle can win potential passengers along the entire route who’s destination station will eventually be reached. To add an additional station inside or outside the circular route a detour would be taken which would increase the coverage of the network (and thus the potential passengers) but also increase the overall time spent by individual passengers en route (and thus decrease the attractiveness). Because of these detours and the non direct nature of the route, the detour ratio (travelled route : direct route) can easily reach 2:1 or 3:1 or higher. The fictional example above does not provide service to the entire city but it does cover a large part of the city with an efficient service.

Example Glasgow Subway

The Glasgow Subway opened in 1896 and not much has changed since then. The 10.5km circular route covers the major points-of-interest in the city, serving about 14 million passengers a year.

To be precise, there are also bus services and there were tram services but I am including this as an example of a Circular Minimal Network because as a single mode of transportation it was planed and built as a lone standing Circular Route. Introducing an initial service with similar route in a city, town or neighbourhood might be a good option.

Train arriving at West Street station. Picture Finlay McWalter

Specialized Transportation Services

Many cities have a tourist bus, boats, (trains) or tram services that by themselves form a Minimal Transit Network.  Often the initial service is introduced as a Circular Route that stops at major attractions which enable visitors to hop and off. One pioneer of such a service are the now standard features of Disney theme parks, the railroad that traverse around the park.

Map of Walt Disney World (Florida) by (WT-shared) LtPowers


Partly an attraction of the park, the railroads (except at Tokyo) also fulfil a public transportation role stopping at 2 to 4 stations around a park.  In the map above, the Walt Disney World Railroad circles the theme park making three stops along the way.

The Lilly Belle locomotive of the WDWRR by Jackdude101

Linear Minimal Network


A Linear Minimal Network (Specialized Network) is often chosen as a solution to connect stations with high potential passenger volumes (town centre, population centres, schools, train station, public services, ect…) to each other. This kind of network can secure a successfully ridership at the expense of coverage by not providing service to areas with fewer potential passengers. A detour ratio close to 1:1 can be achieved by this type of network, making it very attractive for potential passengers lucky enough to be situated near a station.

Example Volschansk Tramway

The Volschansk Tramway consists of one line that connects the southern town of Volchansk and northern town of Lenaya Volchanka. With 7.5km and a hourly service the tramway serves the a town population of 10 400.

Below is a KTM-19, one of the newer trams, leaves the depot.

Voltschansk Tram picture by Oleg NT

Example Serfaus Village Railway

The Serfaus Village Railway follows a 1.3km Linear Route through the car free Serfaus village in Austria. There is no fair to pay by the village inhabitants, hotel guests or visitors that park their vehicles at the parking lot in the east to drive to the ski lift stations in the west.

Sometimes considered the shortest subway in the world it transports 0.83 million passengers per year with a 135 capacity, every 10 minutes and a maximum speed of 40 km/h. It replaced a bus service with similar route in 1986.

Serfaus Dorfbahn Station “Parkplatz” by Basotxerri

Maeander Minimal Network


A Maeander Minimal Network (Circuitous Network) is the travelling salesman problem without being closed into circular route. Often chosen by municipalities wishing to provide services to persons (school children, elderly, tourists, low income, mobility impaired) that do not have the option of individual transport (car, bike, walk). A town council might well put together a list of dispersed points-of-interest that they wish to provide service to, town centre, hospital, school, public park, tourist attraction, population centre, ect… and then route a service to all of these. Alternatively, by many Linear Minimal Network potential passengers and developers lobby for detours to service an additional point-of-interest (e.g. a new retirement home, the city swimming pool) and the network eventually turns into a Maeander Minimal Network. This results in a route that circuitously meanders from one station to the next, which increases the detour ratio and lowers the attractiveness of the transportation network.

Example Ortsbus Flawil

The new Ortsbus Flawil, the village bus service, was introduced in 2013.  It is a Maeander Minimal Network within the town that connects all important destinations with a half hourly service. The route connects the east of the town with train station, it has a short Parallel Section, before connecting the hospital and arcing back to the sport hall before  connecting the school and pensioners home in Lacial Terminal Loop. There are also other pubic transportation options, there is a railway station and bus lines that drive through the town.

The bus, which has 16 seats and additional standing spots, carries on average 392 daily passengers. It has been success, receiving positive response according to InfoWIL’s two year review, regularly at full capacity during the morning hours.

Picture of the Flawil Ortsbus by Niklaus Jung of


Example Sofia Metro

Sofia is currently expanding its metro network but in it’s current form the Sofia Metro  system viewed as separate system, resembles a Maeander Minimal Network. (There are also rail, bus, tram and trolleybus services).

The metro connect many points of interest in Sofia, the railway station,  airport, expo centre, culture palace, university, central grave yard, stadium, ect… The route also intersects itself after following a lacial route in the north. This allows transfer within the system.

Back to an Overview of Network Types.


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