The 30-Minute City: Designing for Access

The 30-Minute City by David M. Levinson
The 30-Minute City by David M. Levinson

Now available for purchase: The 30-Minute City: Designing for Access.

The book reads fast, with just over 20,000 words, and contains 50 images and 6 tables.

About

This book describes how to implement The 30-Minute City.  The first part of the book explains accessibility. We next consider access through history (chapter 2). Access is the driving force behind how cities were built. Its use today is described when looking at access and the Greater Sydney Commission’s plan for Sydney.

We then examine short-run fixes: things that can be done instantaneously, or nearly so, at low budget to restore access for people, which include retiming traffic signals (chapter 3) and deploying bike sharing (chapter 5) supported by protected bike lane networks (chapter 4), as well public transport timetables (chapter 6).

We explore medium-run fixes that include implementing rapid bus networks (chapter 7) and configuring how people get to train stations by foot and on bus (chapter 8).

We turn to longer-run fixes. These are as much policy changes as large investments, and include job/worker balance (chapter 10) and network restructuring (chapter 9) as well as urban restoration (chapter 11), suburban retrofit (chapter 12), and greenfield development (chapter 13).

We conclude with thoughts about the ‘pointlessness’ of cities and how to restructure practice (chapter 14).

The appendices provide detail on access measurement (Appendix A), the idea of accessibility loss (B), valuation (C), the rationale for the 30-minute threshold (D), and reliability (E). It concludes with what should we research (F).

Table of Contents

  • Preface
  • 1  Introduction 15
  • 2  The 30-Minute City: Then and Now 19
  • 3  Traffic Signals 25
  • 4  On the Four Paths 29
  • 5  Bikesharing 35
  • 6  Timetable 37
  • 7  Rapid Bus 39
  • 8  Interface 45
  • 9  Gradial: Or the Unreasonable Network 51
  • 10  Job-Worker Balance 55
  • 11  Urban Restoration 59
  • 12  Retrofit 69
  • 13  Greenfields and Brownfields 75
  • 14  A New Profession: Urban Operations 81

Appendices

  • A  Theory 89
  • B  Accessibility Loss 93
  • C  Access Explains Everything 95
  • D  Why 30 Minutes? 97
  • E  Reliability 99
  • F  Research Agenda 101

FEATURES

  • 114 pages.
  • 50 Mostly Color Images.
  • ISBN: 9781714193660 (Blurb Paperback)
  • ISBN: 9781714193486 (Ingram Trade Paperback)
  • ISBN: 9781714193561 (Ingram Hardcover)
  • ISBN-10:  (Amazon)
  • ISBN-13:  (Amazon)
  • Publisher: Network Design Lab

PURCHASE

Commute Mode Share and Access to Jobs across US Metropolitan Areas

Recently published:

How much of the variation in transit mode share is attributable to accessibility is not well understood, despite its significant policy implications. It is hypothesized that better transit accessibility leads to higher transit mode share. This paper explains block-group level transit mode share using transit accessibility in a logistic model for 48 major US metropolitan areas. Transit accessibility alone explains much of the variation in transit mode share for all 48 regions despite their geographical differences (adjusted R2 0.61, potential accessibility); models for individual cities have stable and interpretable parameters for transit accessibility. The models better explain mode share in cities with higher person weighted transit accessibility and larger populations; an adjusted R2 of 0.76 is achieved for New York City with transit accessibility as the only explanatory variable. Additional automobile accessibility and income variables modestly improve model fit. Time-decay functions fitted to accessibility measures better explain mode choice than the isochrone accessibility, and suggest the catchment area affecting transit mode choice to be within 35 minutes. This work contributes to the understanding of transit mode share by solidifying its link with accessibility, which is determined by the structure of the transport network and land development.

Boston30

How Transit Scaling Shapes Cities

Recently published:

Transit accessibility to jobs (the ease of reaching work opportunities with public transport) affects both residential location and commute mode choice, resulting in gradations of residential land use intensity and transit (public transport) patronage. We propose a scaling model explaining much of the variation in transit use (transit commuters per km2) and residential land use intensity with transit accessibility. We find locations with high transit accessibility consistently have more riders and higher residential density; transit systems that provide greater accessibility and with a larger base for patronage have proportionally more ridership increase per unit of accessibility. All 48 metropolitan statistical areas (MSAs) in our sample have a scaling factor less than 1, so a 1% increase in access to jobs produces less than 1% increase in transit riders; the largest cities have higher scaling factors than smaller cities, indicating returns to scale. The models, derived from a new database of transit accessibility measured for every minute of the peak period over 11 million US census-blocks, and estimated for 48 major cities (MSAs) across the United States, find that jobs within 45 minutes most affect transit rider density. The findings support that transit investment should focus on mature, well-developed regions.

Scaling Coefficients for Transit Commuter and Working Population Density (dot sizes corresponds to residential density); Between-cities scaling (pooling 48 cities) shown with the solid red dot; All cities above the red diagonal line
Scaling Coefficients for Transit Commuter and Working Population Density (dot sizes corresponds to residential density); Between-cities scaling (pooling 48 cities) shown with the solid red dot; All cities above the red diagonal line

Transport Accessibility  Manual Working Group

The Committee of the Transport Accessibility Manual will meet at the Transportation Research Board Annual Meeting in Washington DC in January:

final_cbsa_35620Transport Accessibility Manual Working Group (SAM20-0007 AP050)
Tuesday, Jan 14, 2020  8:00AM  9:45AM (US Eastern Standard Time)

We will be discussing the first (preliminary) draft of the document, which will be distributed to mailing list members before the meeting. Contact me if you would like to be added to the mailing list.

Gradial: Or the Unreasonable Network

The reasonable network adapts itself to the world; the unreasonable one persists in trying to adapt the world to itself. Therefore all progress depends on the unreasonable network.1

The physical location of network infrastructure is one of the most permanent decisions cities make. The Cardo Maximus in the old city of Jerusalem is still a main north-south shopping street, constructed when Emporer Hadrian rebuilt the city in the 130s CE.

The 30-Minute City by David M. Levinson
The 30-Minute City by David M. Levinson 

A street right-of-way, once created is seldom destroyed. A segment of that infrastructure is designed to be optimal at a moment of time, with a particular land use (either the realized development of today or an imagined place of tomorrow), enmeshed within a particular network context of all the other nodes and links, compatible with a particular technology. That it functions at all when land use, networks, and technologies change radically, as they do over centuries, is testament to the general flexibility inherent in networks. But the implication is that if it is optimal for the world in which it was designed, it is unlikely to be optimal as that world changes.

Some adaptations do occur. Streets designed for horses were adapted for streetcars (trams) and bicycles and cars and buses and pedestrians.

Still, it may be the best that can be done. Embedded infrastructure, the dictionary example of sunk costs,2 cannot adapt much to the world around them. Instead we expect the world to adapt to the infrastructure.

Following Shaw, we might say such infrastructures are `unreasonable’, in that they cannot be reasoned with.

Many, if not most, planned cities have been laid out with a network of streets “with the sombre sadness of right-angles,” as Jules Verne, quoting Victor Hugo, described the American grid in Salt Lake City, of streets at 90-degree angles to each other, in his classic road trip story: Around the World in 80 Days. Street grids don’t plan themselves, so while all street grids were planned, not all plans result in street grids.

Organically developed3 cities are often more naturalistic, radial cities, with streets feeding the city from the hinterlands, allowing more than 4-directions of entry. All roads lead to Rome, as the saying goes. The Romans themselves were a bit adverse to this organic radial system once they got their own growth machine going, laying out encampments and new settlements on the grid system. The radial system leading to and from the town would bend once it reached the town gates. But as cities themselves were generally not conceived of as whole, but rather themselves emerged, often as conurbations of smaller settlements, towns, and villages, there are often radial webs centered on town A overlapping radial webs centered on town B. Rome was famously built on seven hills, which can be read as meaning Rome is a conurbation of seven earlier villages. (See Elements of Access, Chapter 3.3)

Each of these networks typologies has its advantages and disadvantages.

DCMetro
Washington DC Metro. The center is a space, not a point. A `triangle’ is formed by L’Enfant Plaza (Yellow/Green with Orange/Blue/Silver), Metro Center (Red with Orange/Blue/Silver), and Gallery Place (Red with Yellow/Green)

 

We observe that radial networks are optimal to maximize access for many-to-one types of movements (suburbs to central city). So rail transit networks, which serve the high loads demanded by, and making possible, high density city centers tend toward being radial. But when they are large they are usually not so radial that all the branches meet at one junction. From a network design perspective, intersecting more than two lines at a station can lead to other types of conflicts, and many systems are designed with triangular center to avoid overloading a single transfer station. Washington DC’s largely radial Metrorail system, shown in  the first figure, illustrates this design. Cities are spaces, not points.

In contrast, the 90-degree grid is reasonably well-suited to maximize access for scattered trips, what network analysts would call a many-to-many pattern. We see this especially in dispersed point-to-point (suburb to suburb, within city to within city) flows that are enabled by and reinforce the grid. This is the network for the automobile. The Los Angeles freeway grid, the famous Milton Keynes arterial grid, and numerous other  late twentieth century cities have been designed in a grid-like way (though not so orthogonal that Victor Hugo would object). Even though the topology is not as efficient from a distance perspective as say a 60-degree mesh, by remaining out of the city core it can keep speeds higher.

But in response to the landscape that emerged with the automobile, transit planners like Jarrett Walker (2012) have called for more grid-like transit networks, so people can move, via public transport, from suburb to suburb without going through the city centre. This is relatively easy to reconfigure for buses, the very definition of  mobile capital, while very difficult for the more capital intensive rail networks with their physically embedded infrastructure.

Still, core radial lines will always be the backbone of transit systems so long as at least one important center justifies a disproportionate amount of service.

So how can we grid the radial, or square the circle, so to speak?

A better network topology might be the 60-degree, hexagonal pattern. (Ben Joseph 2000) But remaking street grids for existing cities is tough-going, as property rights are well established, and requires efforts like those of Haussmann in 19th century Paris. (Willms 1997).

daganzo
Possible system layouts: (a) hub-and-spoke; (b) grid; (c) hybrid. Source: Figure 1 in Daganzo (2010)

Instead, we have overlapping network topologies, ideally which are grade-separated in some fashion, so trains are radial and don’t intersect streets or motorways, and bus services can be more grid-like, and rapid or express bus networks serve the market niche in-between.

Thus the original street level networks are still topologically grids, but the services running on that grid, while still largely parallel and perpendicular, are compressed near the center, so the bus lines, for instance, bend towards the center, as illustrated in the second figure. The regulatory layer of through streets for automobiles may be constructed to defer to the orientation of bus services.

There are no optimal network configurations independent of the enveloping land use pattern or the technological regime. Similarly there are no optimal land use allocations independent of the network pattern or technology. Finally, there is no optimal mode independent of the land use or network. All three of these systems are interlocking. Moving one requires adapting the others.

The unreasonable network forces the land use pattern to adapt to it, such that relocating network elements is more costly than keeping them in place. Similarly, in many ways the network, designed for a given technology, is very hard to adapt to a different technology. That doesn’t stop people and cities from trying, the misfit we see with the automobile in the urban core is the product of failing to acknowledge this unreasonableness. But as the number of European cities restricting cars in the city center are showing, the unreasonable network wins out over technology too.

The Grid/Radial Gradial network is also Gradual. These systems seldom change all-at-once, instead they gradually evolve over decades, centuries, and millenia.


Notes:

1. This is an adaptation of a famous George Bernard Shaw quote.

The reasonable man adapts himself to the world; the  unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.

2. The economist’s adage that “sunk costs are sunk” means that once something has been built, and that money spent, it no longer factors into benefit-cost analysis about how prospective decisions should be made, except to the extent it changes the costs of various options. Logically, you shouldn’t go to a concert just because you bought tickets if you don’t want to go, though if you are considering going to a concert or a bookstore after you bought the tickets, you don’t need to account for paying for the tickets again. You might also consider the `opportunity cost’ of going as the loss from not scalping the tickets. You shouldn’t throw good money after bad. But the sunk infrastructure cannot be unbuilt.

3. Organic development is often largely systematically unplanned, though obviously some degree of planning often goes into laying out a street, even if it is disjoint from any other decisions. When we think of `planning,’ we are generally referring to longer-term more strategic type spatial plans, that consider interactions between prospective decisions, rather than short-term tactical plans that optimize a single decision alone decontextualized from the rest of the city.

Access Across Australia Interview

I was interviewed about our Access Across Australia report by Jane Slack-Smith. It was a really good interview and got into the connections between access and real estate prices. The interview is posted to Facebook, for those of you who use the platform:

Access across Australia: mapping 30-minute cities, how do our capitals compare?

Reprinted from The Conversation.

Accessibility – the ease of reaching valued opportunities such as jobs, workers and shops – is the whole reason cities exist. There is no reason to locate anywhere but to be near things, far from things, or to possess things. Access measures this.

Locations with better accessibility to urban opportunities generally have higher development density and more expensive real estate. This is because places with higher accessibility are more productive, so their workers earn higher wages. And modes of transport that reach more opportunities – that is, provide access to places where people work, live, shop, and more – tend to have higher market share.

Our new report, Access Across Australia, for the first time generates a set of consistent maps and graphs of 30-minute access to jobs and workers by each transport mode for each of the eight capital cities. This covers around 70% of the nation’s resident workers and employment opportunities.

The full report compares 10-minute to 60-minute accessibility to both employment locations and to workers’ homes by four modes of transport – car, public transport, walking, and cycling – for each city. It also reports the overall job-worker balance, comparing how many workplaces can be reached to how many competing workers want to reach those same workplaces.

The accessibility measures take into account the effects on travel times of traffic congestion and the walking and transfer elements of the public transport mode.

Accessibility captures the combined effect of land use and transport infrastructure. The faster and more direct the network, the higher the access. The more opportunities (people and places) that can be reached, the higher the accessibility.

This value varies across and between regions. For this article, we show this in maps for Sydney – the full report has maps for all four transport modes, for both jobs and labour (resident workers), for all eight cities. In the table, city-level accessibility numbers are reported as a metropolitan average, weighted by the number of people who experience that accessibility (population-weighted accessibility), to best represent the experience of the working population.

Population-weighted 30-minute accessibility to jobs; cities ranked by the size of employment opportunities. Hao Wu and David Levinson

The rankings in the table are discussed below for each mode.

Cars

Cars have higher accessibility than public transport, walking, or cycling. Perth has the greatest number of jobs and workers reachable by car within 30 minutes.

At time thresholds of 40 minutes and longer, residents of Sydney and Melbourne have higher accessibility than other cities. During the morning peak period, Melbourne has moderately better car accessibility than Sydney, despite Sydney being larger and having more opportunities overall. This indicates that roads in Melbourne are faster than those in Sydney.

30-minute job accessibility by car in Sydney. Hao Wu and David Levinson

 

Public transport

Public transport accessibility incorporates time to reach transit stops and station on foot, and equals the minimum of walking and transit times between an origin and destination. It remains at a significant disadvantage compared to car travel, reaching between 12% and 18% of the urban opportunities accessible by car under a 30-minute threshold.

Public transport accessibility tends to be high in city centres and low in other places. The disparity with cars peaks at 20-30 minutes’ travel time.

Sydney and Melbourne have the best public transport accessibility among Australian cities, followed by Perth and Brisbane. It could be higher still with better-located station entrances and exits.

30-minute job accessibility by public transport in Sydney. Hao Wu and David Levinson

 

Cycling

This report identifies cycling as a viable option for improving accessibility. Assuming cyclists are willing to ride on the street, people cycling can reach about twice as many jobs as people on public transport within 30 minutes in all eight Australian cities, and around one-third of job opportunities reachable by car (except for Perth, which is 16%). Sydney and Melbourne have the highest cycling accessibility.

Of course, it should be recognised that many potential bicyclists are extremely uncomfortable riding in traffic. Their accessibility on a more limited network of residential streets and protected bike lanes would be much reduced.

30-minute job accessibility by cycling in Sydney. Hao Wu and David Levinson

Walking

People walking cannot travel as fast as those on other modes, particularly over longer distances, where public transport and cars can travel at much higher speeds. Not surprisingly, walking has the lowest accessibility of all four modes. The presence and timing of traffic signals that give priority to cars significantly reduces walking accessibility.

Walking accessibility is closely related to urban density. City centres, especially those in larger and denser cities, tend to have better walking accessibility.

Among the eight major Australian cities, Sydney and Melbourne have the best walking accessibility. Hobart and Darwin have the lowest.

30-minute job accessibility by walking in Sydney. Hao Wu and David Levinson

Job-worker balance

The job-worker balance of a place is measured dynamically as the ratio of jobs and resident workers reachable within 30 minutes. City centres have superior accessibility to both jobs and workers, and less pronounced advantage in car accessibility compared to other modes. Higher jobs-to-workers accessibility ratios in city centres show that, in general, jobs are distributed closer to and better connected with city centres than residential locations.

The job-worker balance is a potent indicator for identifying urban centres and for measuring the strength of centres.

Ratio of 30-minute job accessibility to worker accessibility by car in Sydney. Hao Wu and David Levinson

Conclusions

This research gives us a baseline accessibility measurement using the best available data for 2018. Repeating this analysis over time will enable long-run tracking of accessibility as a performance measure.

This will enable us to answer questions such as: is accessibility by a particular transport mode rising or falling? Is that due to congestion, network contraction, new infrastructure, or changes in residential or employment density? Are policies working to expand accessibility for the population as a whole, and for areas within cities? Which investments give the most accessibility “bang for the buck”?

Some of the results are surprising – in particular, the observation that the speed of Perth’s freeway and street network more than compensates for more limited scale in producing 30-minute car accessibility.

But this result is just an indicator of broader accessibility, which includes additional relevant opportunities, more times of day and more information than is presently at hand. This is likely to become more widely available in an era of big data if governments choose to actually implement the open data claims they advertise.

Transport Poverty| A Political Economy of Access

We are pleased to make available Chapter 21: Transport Poverty of A Political Economy of Access. It opens:

A Political Economy of Access: Infrastructure, Networks, Cities, and Institutions by David M. Levinson and David A. King
A Political Economy of Access: Infrastructure, Networks, Cities, and Institutions by David M. Levinson and David A. King

When we talk about access as a value that should guide transport policy, we need to address access for whom, not just access to where by what mode. In the auto-dependent US, the mode that offers the most access in most places currently is the car. Yet cars are expensive, and many people struggle with basic access (and mobility) simply because they can’t afford it. Transport is the second largest spending category for US households, behind only housing. This is the case even as transport is heavily subsidized, regardless of mode.1 As discussed in Subsidy,2 the general approach is to spread whatever help is offered thinly across infrastructure capital investment. This does little to help those with the least.

How close is Sydney to the vision of creating three 30-minute cities?

This article, by Somwrita Sarkar, Hao Wu, and David Levinson first appeared in The Conversation.

The Greater Sydney Commission has proposed a 40-year vision of a metropolitan region formed of three “cities”: the Eastern “Harbour” City, the Central “River” City, and the Western “Parkland” City. The plan aims to create 30-minute cities, where the community has access to jobs and services in three largely self-contained but connected regions. Thus, Sydney would be polycentric.

The Greater Sydney Commission’s Three Cities Plan. Greater Sydney Commission

A polycentric city has multiple centres of employment, economic or social activity. Local labour markets and residential zones minimise long commutes, create a sense of place and neighbourhood, and strengthen economic agglomeration as companies, services and industries benefit from being close to one another.

However, it is still unclear whether Sydney is actually moving towards such a structure. In our recent work, we developed new ways of measuring polycentricity. We applied these to Journey to Work data from the 2016 Census to test how consistent the current centricity patterns of Greater Sydney are with the proposed plan.

How do you measure polycentricity?

Traditionally, employment densities are used as a measure of polycentricity. If the density of jobs in a location is higher than the average density for the entire region, then it is a centre.

However, this simple measure misses a key notion that makes cities what they are: network flows and spatial interactions. People “flow” from one place to another. Employment centres “attract” flows, and residential areas “produce” flows. Thus, a city is a collection of locations that interact dynamically, connected by daily commuting flows.

We proposed a set of new metrics to capture this idea of flows. We defined the net inflow of people to a location as the total number coming to this location to work minus the total number going from this location to work elsewhere. If the net inflows are positive, this place is a centre.

The chart below illustrates the idea. The base arc on the circle shows the number of people “flowing” out of a location to another location. The connecting arcs are coloured black if the net inflows into the focus regions (a), (b) or (c) are positive.

Testing polycentricity via net inflows: (a) Sydney City and Inner South (Sydney CBD), (b) Parramatta, (c) Eastern Suburbs. Source: The authors

Sydney CBD clearly emerges as a global centre for the whole region. Parramatta is a regional centre. Other locations such as the Eastern Suburbs are not centres at all.

The net inflow to a location can be divided by the total number of trips in the system, so inflow values are scaled from 0 to 1 using a standard statistical procedure. The higher the value, the higher the centre’s rank in the urban system. Here, a score of 1 means the centre is an absolute: all the trips in the system are a net inflow into the centre.

This gives us a trip-based centricity measure. And based on the area of the location, we can calculate a density-based centricity measure.

The maps below show trip-and-density-based measures – (a) and (b) respectively – for Greater Sydney at the Statistical Area Level 2 (representing a community that interacts together socially and economically).

Note the dominant role of the Sydney CBD. The other centres emerge as weak centres. Also, many of the second-order centres are very close to the CBD.

Visualising polycentricity in Sydney (red indicates highest values): (a) trip-based centricity, (b) density-based centricity, (c) transit-accessibility-based centricity, and (d) auto-accessibility-based centricity. Source: The Authors

The concept of accessibility

Counting the net inflow into a location may provide us with information about general centricity. However, it still does not tell us how easy or difficult it is for people to actually get to jobs. This brings us to the idea of accessibility.

Walter Hansen defined accessibility as “the spatial distribution of activities about a point, adjusted for the ability and the desire of people … to overcome spatial separation”. More practically speaking, a location is accessible if it can be reached within a set time (say 30 minutes) from another location.

We counted the net accessibility of a location by counting the number of jobs minus the number of workers (labour) that could be accessed from a particular location (SA2) in Sydney within 30 minutes. We counted travel time both by car and by public transport during a usual weekday peak hour (Wednesday 8am). Similar to the trip and density measures, accessibility centricities can also be scaled as values between 0 and 1. This allows us to compare across the four measures.

In the maps above, (c) and (d) show the transit and auto-based accessibility centricities based on accessibility for public transport and vehicles. Sydney CBD is highly accessible. The second-order centres show much weaker accessibility.

Takeaways for urban policy and the three-cities plan

The chart below shows the top-ranked centre, Sydney CBD (Level 1 centre), and the lower-ranked subcentres (Levels 2 and 3) emerging from our analysis.

Identified Level 1, 2, and 3 Centres for the Greater Sydney metropolitan region. Source: Authors

Accessibility planning should guide the design of a polycentric city

The design of polycentric Sydney should be guided by accessibility, the locations of jobs and homes, and subregional labour market organisation.

In short, the region should give priority to making jobs accessible by locating new jobs in emerging centres, instead of a mobility-focused system that takes people to jobs.

Reduce spatial mismatches between jobs and homes

Our results show that Sydney, paradoxically, remains strongly monocentric and strongly dispersed at the same time. The Sydney CBD accounts for 15% of jobs in the region, with the remaining 85% of jobs scattered around in weaker second-order centres and non-centres. Positive correlations exist between percentage of employed workers, trip-based centricity and the subcentre ranks.

But we see significant disparities between these ranks and accessibility centricities. This shows the spatial mismatches for commute lengths in the system.

A subcentre with high trip-centricity, employing a high percentage of workers, but relatively lower auto- and transit-based accessibility centricity, implies that even though a significant percentage of the population comes to this location to work, access to jobs at this centre within 30 minutes is low.

A policy response would be to increase the accessibility of jobs from this location, as it already serves as a centre. This situation is particularly clear in the cases of Parramatta-Rosehill and Macquarie Park-Marsfield. Penrith and Liverpool too have extremely weak accessibility centricity.

Parramatta CBD is emerging as a secondary centre in the Greater Sydney region, but with much weaker accessibility of jobs than Sydney CBD.haireena/Shutterstock

 

Polycentric cities should promote spatial justice

As cities grow in size, commute lengths increase if the labour market for the entire metropolitan region is integrated. Commute lengths will stabilise if a city has a clear polycentric or modular structure.

In the case of Sydney, spatial equity has always been a concern. However, inter-city comparisons show city size has a strong bearing on its equity and efficiency.

Our results show it’s increasingly important for larger cities to introduce a framework of subregional labour markets as part of the polycentricity agenda. Enabling shorter commutes for workers will improve spatial equity as well as efficiencies.

 

The article is based on this paper: Sarkar, Somwrita, Wu, Hao and Levinson, D. (2019) Measuring polycentricity via network flows, spatial interaction, and percolationUrban Studies. [doi])