These data provide some snapshots of the spatial distribution of people in the city at successive points in time. We have this information for the 31 Spanish urban areas of more than , inhabitants, and for 55 days. These percentages are almost the same for all the urban areas. The choice of the spatial scale of data aggregation is known to be an important source of bias in spatial analysis 25 , hence we tested the robustness of our results on three different sizes of grid cells see section Methods for details.

The white area represents the metropolitan area administrative delimitation , the brown area represents territories surrounding the metropolitan area and the blue area the sea. In order to get a preliminary grasp of the data we plot the time evolution of the number of users along the day and see if it follows the same pattern in every city. Figure 4 shows the average number of mobile phone users per hour according to the day of the week for six of them.

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Globally, the number of phone users is significantly higher during the weekdays than during the weekends, except at night time. From 11pm to 8am, the number of users is relatively low, it reaches a minimum at 5am during weekdays and at 7am during the weekend. For all cities we observe two activity peaks, one at 12am during weekdays 1pm during the weekend and another one at 6pm during weekdays and at 8pm during the weekend. In order to compare these values obtained for different cities, we rescale the values by the total number of users for an average weekday.

We show the results in Figure 5. The data collapse is very good in the morning, while in the afternoon we observe a little more variability from one city to another. It is interesting to note that in four cities located in the western part of Andalusia Sevilla, Granada, Cordoba and Jerez de la Frontera the activity restarts later in the afternoon, around 5pm one hour later than in the other cities. Time evolution of the number of mobile phone users per hour during an average weekday a Total number of unique mobile phone users per hour shown here for the eight biggest Spanish cities.

Each value U i t is equal to the number of phone users in city i at time t , N i t , divided by the total number of phone users in i during the entire day:. The good collapse suggests the existence of an urban rhythm common to all cities. The difficulty is then to study this complex object which displays variation in time and space. We will consider here two main directions to tackle this problem. The first one is to define global indicators that consider all points and weight them by the user density.

There are pros and cons in each method. Looking at hotspots is convenient since it provides a clear picture of the important locations in the city, but contains some arbitrariness in their determination.

## INTRODUCTION

On the other hand, working with weighted indices does not require to identify hotspots but at the cost of producing results more difficult to interpret. This is why in the following we will successively apply the two methods. The average weighted distance D V t between individuals in the city see section Methods for the precise definition and its evolution during the course of an average weekday provides a first interesting indicator about the organization of the city.

Figure 6 a shows the evolution of this normalized average, weighted distance during a typical weekday. We can essentially distinguish two broad categories according to the spatial organization of residences and activities:. In the case of the simple picture of a typical monocentric city with predominant Central Business District CBD , the city collapses in the morning when people living in the suburbs commute to their workplaces, and expands in the evening when they get back home.

We then expect in this case a large variation at the city scale of the average distance D V. For more polycentric cities, where residential and work places are spatially less separated, we expect a smaller variation of D V than the one observed for monocentric cities. This distance D V is equal to the average of the distances between each pair of cells weighted by the density of each of the cells. The resulting distance is then divided by the typical spatial size of the city given by the square root of the city's area in order to compare the curves across cities.

For all cities we observe the same typical pattern: we see two peaks, one around 7 am, when people switch on their mobile phones, probably at home or when they are in transportation system's entry points see Figure 6 a. During the afternoon we see a second, smaller peak dispersed over 4—5pm, when people start going back home. This afternoon peak is less pronounced, suggesting a higher variety of mobility behaviors at the end of the day. The interesting feature of theses curves is the variation amplitude that informs us about the importance of this collapse phenomenon.

## INTRODUCTION

Despite the fact that several factors such as phone use or behavioral factors affect these variations, we observe a common pattern: a pronounced peak at the beginning of the day and a minimum usually observed at the middle of the day. This means that whatever the hour of the day, the spatial spread of the high density locations does not change significantly. High density locations correspond to different activities depending on the moment of the day, and a small value of the dilatation coefficient implies that daytime activity places work places, schools, leisure places are not more spatially concentrated than residences.

In the opposite case of large values, the spatial organization of the different high-density locations changes significantly along the day. A typical example would be a monocentric city where individuals are localized in the CBD during the day and where residences are spread all around the center. In our set, Zaragoza for example is representative of this type of cities. For the intermediate group the cities display a less marked behavior, probably resulting of a combination of monocentric and polycentric features. This problem corresponds to identify local maxima in the surface of density of users.

In contrast here all technical details can be found in the Methods section , we discuss two extreme choices for the threshold value. We first focus on the number of hotspots. This measure is motivated by recent theoretical and empirical work 29 that has highlighted a clear sub-linear relation between the population size of cities and their number of activity centers defined as employment hotspots.

For the U. Figure 7 displays the number H of hotspots versus the population for the set of the 31 biggest Spanish cities considered here. The power law fit confirms the result obtained in 29 that there is a sublinear relation and, remarkably enough, that the value of the exponent is of the same order. We note here that this result is robust against the thresholding criteria used to define hotspots see also section Methods for aggregation grids with different cell sizes. We also note here that recent empirical work 30 has highlighted the sensitivity of the values of scaling laws exponents to the choice of city boundaries.

This result underlines the crucial role of city definition when attempting to identify patterns of behavior across cities, and the need for consistency in defining the spatial boundaries of cities for such comparisons That is the reason that has led us to rely on the spatial delimitations of urban areas , which are harmonized delimitations based on the ratio of home-work commuting journeys see Methods for details.

Each point in the scatterplot corresponds to the average number of hotspots determined for each one-hour time bin of a weekday for five weekdays considered here. The power law fit is consistent, for both hotspots identification methods, with a sublinear behavior characterized by an exponent of order 0.

This figure was created with R. Another interesting feature to inspect in cities is the stability of their hotspots and the evolution of their relative importance in the city according to the hour of the day, which is related to the evolution of the hierarchy of places in the city. In order to capture the behavior of cities about these aspects, we plot various indicators.

We start with the histogram of the persistence of hotspots: for each city we count the number of one-hour time bins during which each cell has been a hotspot. The permanent hotspots are the most important locations in the city in terms of individuals density. An interesting question is whether their rank according to the density is constant or changes during the day. Our results show that the heart of the cities is indeed very stable both in space and in time, whatever their size.

Another important question about hotspots concerns their spatial organization. We compute how distant they are from each other, compared to the typical size of the city given by , where A is the city's area. This indicator informs us how the permanent hotspots are sprawled all over the city's space, and it is thus a measure of the compacity of the city core: for cities with values around 0, the permanent hotspots are very close to one another, when compared to the spatial extension of the urban area. On the contrary, a value close to one indicates that these always-crowded places are spread all over the whole city space see figure 9.

It is interesting to note in Figure 9 b that the compacity of a city seems to increase with the population size.

At least for a large subset of cities, we indeed observe this trend, which is consistent with the idea that the larger the city, the more spread are the hotspots and the more polycentric it tends to be. Rank plot of the compacity coefficient among the 31 metropolitan areas. We observe a trend at least for a large subset of cities, the corresponding fit is shown as a guide to the eye.

These figures reveal two types of spatial organization: polycentric in the case of Bilbao c , whose permanent hotspots are not contiguous and more spread over the space of the urban area, and clearly compact and monocentric in the case of Vigo d The maps c and d were generated with R standard packages for handling spatial data and make use of freely available vector layers.

## Mapping Urban Practices through Mobile Phone Data | Environment & Urbanization

For each city, once we have determined the hotspots and have classified them into permanent, intermediary and intermittent, we measure the average distance between hotspots within each group. Since the intermittent hotspots are those with a lifespan of six hours at most, they are more inclined to capture the residential locations, while the permanent hotspots represent the dominant places of the city, that is, zones that are very dense both during daytime and nightime.

On Figure 10 a we plot the histogram of this ratio for all cities, for the two hotspots delimitation criteria see section Methods for these plots with different sizes of the aggregation grid.

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We can see in this plot that the distribution is centered around 0. We also computed the ratio of the average distance between intermittent hotspots and the average distance between intermediary hotspots i. We plot the histogram of this ratio for all 31 cities in Figure 10 b. The distribution is peaked around 0. While the spatial features of intermittent and intermediary hotspots are similar, the main difference between cities lies in how the permanent hotspots are distributed in space.

We have shown in this study that it is possible to extract relevant information from mobile phone data, not only about the mobility behavior of individuals, but also about the structure of the city itself.

We have defined various indices that allow us to characterize some dynamical morphological properties of cities, including the evolving average distance between individuals in the city through the course of the day. Such dynamical properties can serve as a basis to propose new classifications of cities. We have also presented a generic method to determine the dominant centers, the hotspots, and we have confirmed recent results -obtained on completely different data- showing that the number of activity centers in cities scales sublinearly with the population size of the city.

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We have also highlighted some properties of hotspots in Spanish cities, such as the strong stability of the hierarchy of the hotspots along the day, whatever the city size. These results constitute a step towards a quantitative typology of cities and their spatial structure, an important ingredient in the construction of a science of cities.

They also raise questions that could be adressed in future studies. In particular, we could ask if these morphological patterns are universal, and to what extent they are specific to Spanish cities. More generally, they might be specific to european cities whose urbanization history is older than in other continents, resulting in urban systems with specific morphological properties 14 , Also, it would be interesting to investigate if the time dynamics observed here are similar in cities of recently urbanized and fast growing regions.