A city is full of barriers that limit human mobility, some are visible, some are not. Administrative boundaries, natural obstacles, railways, roads: all can act as a barrier. In this study we introduce two indicators to quantify the barrier effect.
A network science framework is presented to quantify barrier effects in urban mobility.
Not just the physical barriers, but the administrative boundaries also limit urban mobility.
The hierarchy of urban barriers are reflected by the communities of the mobility network.
Urban barriers have significantly different effects by people's home location and the amenity complexity of destinations.
How can you use a network to characterize the barriers of an urban landscape? A city's got all sorts of networks: roads, public transport, public utilities and so on. Yet, we build a different one based on how people move around in the city. A lot of smartphone apps and the services that power them collect geographic locations. Some companies collect this location info and provide it for research purposes. The mobile positioning data record includes a timestamp, a device ID, and a GPS location. These appearances are clustered into "stops", where someone spent some time. Then, every stop is mapped to a block of the city (as the figure shows), and considered a node of the network. The blocks are connected by edges if someone stops in two blocks in a row within a day.
There's a pretty cool technique called community detection, that can identify densely connected parts of a network that are loosely connected to each other.
A densely connected part is called a community, but what's more important right now is that the loosely connected path between them is a barrier.
The figure shows two communities in Budapest.
The barrier between them is the district boundary between District 4 (pink) and 15 (gray), as the pink one matched with District 4 and the gray one with District 15.
The connections between the communities depicted by yellow.
It was previously mentioned that communities match with districts.
Is there a way to measure this match?
Imagine two overlapping shapes, and the question is how well they match.
If we rephrase the question, we want to know how big the non-matching parts are compared to the matching ones.
For example, there's the community area, which is outside the districts, and then there's the district area, which isn't covered by the community.
Luckily, there's already a method in mathematics that can give an answer to the rephrased question, and it's called the symmetric difference.
The area of the blocks that are clustered as a community, but outside the target district, as well as the area of the district that isn't covered by the community is summarized as a measure.
We call it Symmetric Area Difference.
Lower values of this index mean that the detected mobility clusters fit better to urban boundaries, since the error of the matching (the area of the non-matching parts) is smaller.
The figure on the right shows this method.
We've got a district with yellow, and a community with orange.
They overlap, but a big part of the district isn't covered, and at the same time, the community covers quite some area that doesn't belong to the district.
We know how communities and barriers are identified, but do they always look the same?
Well, the short answer is no.
The barrier is a loose connection between two densely connected part of the network, but what does "loose" mean in this case?
We used the Louvain community detection method, which has a parameter, called resolution (γ), which describes the how loose an inter-community connection should be to interpret it as a barrier.
Here's an example of District 15 (the gray one we talked about before).
Each figure shows the resolution value in the top-left corner, and the Symmetric Area Difference (SAD) from the last section compared to the resolution in the top-right corner.
The main part of the figure compares the community to the district boundary.
At first, the community is way bigger than the district because the resolution value is really small.
As we increase the resolution, the community and the district match at γ = 4.0.
You can see that only a tiny bit of the district isn't covered by the community, and at the same time, barely any blocks belong to the community outside of the district.
The total area of the community is pretty much the same as the district, so the SAD is almost zero (see the top-right corners of the figures below).
The good fit lasts for a while (until about γ = 6.5), but then something happens.
The community is split into two parts: a bigger (green) and a smaller (blue) community.
Later on, the blue one later tries to extend to cover all the remaining area.
The M3 motorway is responsible for all of this.
The motorway divides the district into two parts and the network reflects to this.
If we make the community detection to be more sensitive by increasing the resolution, it'll detect weaker barriers as well.
As you can see in the figures below, the boundaries of the District 15 are still barriers, strong enough to limit the communities.
But then something new comes into the game: the motorway.
Now, that we've looked at the barrier effect using a network-science approach, let's lake a look at how it affects the people living in the city.
Let's focus on the individual trips in the city, and keep track of any barrier crossings (like district boundaries, busy multilane roads, railways, or rivers).
Also, count it if a barrier crossing is also a community crossing.
Check out the figure on the left to see what I mean.
Then, we calculate the fraction of the barrier and the community crosses among all barrier crossings (separately by barrier types of districts, neighborhoods, primary roads, secondary roads, railways, and rivers), and take the inverse of this ratio.
We call this measure, the Barrier Crossing Ratio, which describes that how much a given type of barrier affects to people.
Budapest is divided by the river Danube, so it's an obvious barrier, but not every barrier is supposed to affects everyone the same way.
We've got to do this for different resolution values, because the communities are formed differently at different resolutions, as we saw before.
You might be wondering why this is important.
Well, it gets interesting, when we sort people into different groups and take a look at how a given barrier affects these groups.
Let's look at an example, focusing on people's mobility habits in Budapest and grouping them into groups based on where they live.
The Central Statistical Office of Hungary defines seven district groups in Budapest (pink) and six sectors of the agglomeration (green).
The people whose mobility patterns construct the network, are clustered into thirteen groups, based on their home locations.
The results are displayed in the figure below, which shows the Barrier Crossing Ratio in contrast to the resolution by the six types of barriers, and by the home location group of the individuals.
Just a heads-up: a smaller Barrier Crossing Ratio (BCR) indicates a stronger barrier effect.
Our experiment shows that people living in Budapest experience a stronger barrier effect considering with every barrier type.
This might sound a bit crazy, right?
People living in the agglomeration usually have longer commutes, while crossing administrative boundaries, roads, and maybe even the river.
This actually lines up pretty well with previous studies and also the common sense.
Studies have shown that people living in the center of a city tend to concentrate their lives in a smaller area, because city centers usually provide all the necessary services.
If someone rarely leaves their neighborhood, they rarely cross barriers.
If they don't cross barriers, their movement stays within the densely connected community.
In other words, the barrier between the communities feels strong to them.
And don't forget that roads are usually built to connect places, not to divide people.
Some of these barriers are actually help people living in the agglomeration to reach their destinations.
Basically, they help break down barriers.