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On Hypo- and Hyper-connectivity in Transport
Connectivity is good. Is more connectivity better?
During the early stages of a useful technology like roads or transit, adding links generally adds more benefits than costs. However there are limits. A four way intersection is good does not mean a five way intersection (or six or seven) is necessarily better. The more complex intersection adds to the friction of travel and cost of construction over its simpler alternatives.
Muller's Hexagonal Network
A grid network, with streets at 90-degree angles to each other might not be as good as a network with streets at 60-degree angles, which reduces travel costs and increases directness (reduces circuity), but it is most assuredly better than a fine mesh with streets at 10-degrees or 1-degree, where almost all is pavement and little is actually buildable land. While 1-degree network would reduce surface travel distance, it does so at many other costs, including a reduction in accessibility because of fewer development opportunities.
Consider the circuity additions based on network angle. If all places are connected via a 90-degree square grid, the circuity at worst is SQRT(2), but on average 1.21. So travel distance increases by 21% over a straight-line path. With a 60-degree grid, the circuity is lower, at worst 1.22, on average nearer 1.11. (Bus transit networks, which tend not to follow the shortest path, have much worse circuity.)
The optimal level of connectivity depends on what you are trying to optimize.
Hypo and Hyper are antonyms. Wiktionary says:
I would maintain that most developed countries are pretty close to optimal in terms of road connectivity, that there are few missing links whose costs outweigh their benefits. If subsidies for modes were to be eliminated, some large cities might be under-developed in terms of transit connectivity because of a bias towards coverage (and circuity) aims rather than frequency.
Let's think of this in the context of induced demand. More connectivity in one sense means a faster network, which users exploit by traveling longer distances in the same amount of time. They gain utility by being in a house they prefer. However they use up the capacity gains of the network. But more connectivity increases the friction of connections (junctions, interchanges, transfers) which slows down the network. Induced demand due to connectivity is thus self-limiting.
Braess Paradox is the most famous supply side example of hyper-connectivity. In this situation, removing a link improves travel for road users at large because the additional network link induces travelers to use a link with a lower average cost but higher social marginal cost.
A key point is that whether a network is over or under-connected depends on the technology of travel, as well as the amount. A network which is overconnected for cars may be underconnected for pedestrians who don't congest so easily. A network which is overconnected for 2000 cars may be underconnected for 1000. This is the challenge in building cities. Networks last for seemingly forever, but technologies that use them change more frequently. How can you design a permanent infrastructure flexible enough to serve future technology?