Visual Analysis to Assess Attraction and Organisation of Contemporary Metropolitan Systems—A Case Study of Central and Northern Italy

Abstract

The landscape of scientific research is rich with experiments aimed at identifying polycentric morphologies, defining their degree of polycentricity, and the socio-economic and environmental relationships that develop within them. However, some aspects are still under-researched, such as defining a procedure for determining the extent of the metropolitan area of influence. This research aims to experiment with a graphical–analytical methodology aimed at identifying and representing the functional area of metropolises, i.e., the territorial limit beyond which a metropolis’ attractiveness ceases to exert its territorial influence, and which also allows the territorial ramification of urban cores with greater attractiveness to be determined and visualized graphically. Using Visual Analytics as a conceptual basis, it is possible to combine methods and technologies that harness the potential of human understanding with the increased capabilities of electronic data processing for a more adequate understanding of the research scope. For this research, the graph-analytic mix adopted comprises the graph theory algorithms for the analytical quantification of relationships and the reference surface area of polycentric metropolises. In contrast, the subsequent visualisation of relationships and their spatial branching is based on the electronic evolution of graphical techniques based on the works of Henry Drury Harness and Charles Joseph Minard, particularly those invented to map commuter flows and migrations. The research results, focusing on Northern Italy, demonstrate a highly interconnected and polycentric system, with macro-areas whose functional boundaries seldom coincide with the administrative boundaries of the regions. The research demonstrates the existence of five territorial macro-regions encompassing the 11 regions outlined in the Italian state’s legislation, containing polycentric metropolitan systems with distributional characteristics that differ from each other.

1. Introduction

1.1. The Polycentric Metropolis

The contemporary metropolis can create new and changing economic and political geographies that significantly influence the development of regions and continents [1]. The relationships between urban form and well-being, economic growth, and sustainability within polycentric metropolises are subjects of strong interest among a growing and multifaceted scientific community. Some have delved into the analysis of economic, environmental, and social externalities arising from metropolitan ‘forms’ [2,3], while other research is focused on developing territorial policies to enhance the competitiveness, vitality, social cohesion, and environmental sustainability of metropolises [4]. Still, others are directed towards understanding the connections between metropolitan form, commuting patterns, and sustainability [5]. Several studies argue that polycentricity promotes resilient, sustainable, and well-organized cities. According to several studies, cities become less vulnerable to single points of failure by dispersing their centres of activity and development. In the event of a disturbance or crisis, such as natural disasters or economic downturns, a polycentric city can better absorb shocks and distribute the impacts more evenly across its multiple centres [6]. This enhances the city’s ability to recover and adapt over time. Sustainable urban development requires the efficient use of resources and reduced environmental impact. Polycentric morphologies promote sustainability by minimising the need for extensive transportation networks and reducing energy consumption. Concentrating services, amenities, and employment opportunities in multiple centres reduce the reliance on long-distance commuting, which, in turn, decreases traffic congestion and lowers carbon emissions [3]. Understanding and implementing polycentric morphologies contribute to more efficient land use. Rather than having a single central business district, a polycentric city can distribute commercial, residential, and recreational areas across multiple hubs. Therefore, this approach could optimise land utilisation, reduce sprawl, and foster a more balanced distribution of amenities and services, creating a more liveable environment for residents although polycentric urban development is sometimes considered to be important but not sufficient [7].

Numerous studies have already demonstrated the growing trend of urban systems towards polycentric forms, which replaced the monocentric morphology of the previous industrial city [8,9] within larger and more complex territorial contexts defined as mega-regions. In these mega-regions, urban centres are interconnected through economics, infrastructure, the environment, information, land use, culture, and history [10]. Polycentric metropolitan areas are typically composed of densely populated urban centres with significant attracting power referred to as “mother cities”, and the surrounding sparsely populated, interconnected areas constitute a constellation of “child centres” that rely on the main urban centres for functions, services, and employment [11]. The concept of polycentricity originates from studies on public policy, tracing back to the early work of economist Polanyi in 1951 [12], who defined two primary forms of social organisation called the “commanding order” and “polycentric order”. These differ in how economic and social actors interact to decide how to utilize resources [5]. Subsequently, the concept of polycentricity has been applied in different disciplines, obviously with different connotations; for example, in the field of spatial planning, the studies of Gordon et al. [13] define the concept of “polycentric city” based on the employment level of different centres and how they tend to influence each other. The subsequent development of the urban theory of polycentricity has gradually stimulated the application of polycentric spatial governance models that underlie the growth of mega-cities and mega-regions. Some significant examples in this direction are the Beijing General Plan for Urban Development, known as Beijing Urban Overall Planning 2016–2035, in which several sub-centres of Beijing are defined and the main functions are assigned to them, such as the Shijingshan Districts as a centre for technological innovation [14]. Also, on the Asian continent, the Plan for the Yangtze River Delta (Planning of the Yangtze River Delta) provides a clear functional division within the mega-region with centres such as Hangzhou earmarked to develop financial activities. In contrast, others are earmarked for developing manufacturing and shipping activities [15]. In Europe, London’s South East Plan envisions mega-city growth by densifying the outer, less populated centres by improving transportation efficiency within the mega-region [16]. The “ring city” in the Netherlands, referred to as the Randstad, encompasses 17 cities interconnected by integrated road, rail, and river infrastructure [17], with Amsterdam representing the political and technological development centre, Rotterdam specialising in maritime trade due to its port, Utrecht specialising in tourism activities, and Leiden oriented to scientific research. In North America, the implementation of the America 2050 Plan is based on the study of critical factors such as topographical features, economic and environmental infrastructure systems, and cultural and historical aspects, which are considered strategic for developing mega-regions [18].

1.2. The Study and Representation of Polycentricity

In the literature, several methodologies enable the identification of polarities within a mega-region; others have been developed to define the morphology and degree of polycentricity, and others have been developed to understand the dynamics and relationships that develop within them [19,20]. For quite a long time, researchers have mainly focused on identifying “centralities”, that is, urban cores characterized by a concentration of polarising economic agents around which metropolitan networks differing in size and hierarchy are organized [21]. The earliest research can be traced back to the pioneering work of Christaller in 1933 (Figure 1) and Lösch in 1940 [18,22], who discovered the correlation between urban size and the numerosity of economic activities, but more importantly, they could first observe a hierarchical and regular spatial distribution among urban centres, where equal size class of urban cores corresponds to a similar equidistance between centres [23].

Following the research by Christaller and Lösch, researchers shifted their focus towards developing what we could call static methodologies. These methodologies primarily consider the spatial distribution of employment or population within macro-regions, with limited emphasis on analysing interactions between urban nodes. Recently, some methodologies based on functional approaches have been developed particularly for the analysis of commuting between urban cores as a reflection of the different allocation of resources in the territory [11,25,26,27]. For example, some studies have analysed metropolitan morphologies and their polycentric character by applying gravitational models [28]; at the same time, various indices have been developed and applied to measure centrality and identify secondary cores, for example, through the ratio of commuter flows or employment between the central city and the rest of the mega-region, or the ratio of commuters from other mega-regions to total employment [3,9,27,29].

Specifically, graph theory, in conjunction with the exponential growth in computational capacity, provides analytical tools not available in other methodologies. It allows for calculating mutual influence among various nodes in the network, considering hundreds of thousands of relationships, each with different weights and directions (Figure 2). Another no less important aspect of the need to determine centralities concerns the determination of the edges of the metropolis—that is, the limits within which these relationships develop and possess a significant capacity to influence the territory and the resources it contains. The contemporary metropolis, made up of fundamental physical elements but especially intangible relationships, does not have a defined or immediately recognizable boundary; therefore, the problem of determining these limits arises [30]. This aspect is fundamentally crucial in socio-economic, demographic, environmental, and spatial analyses [21]. Often, the boundaries of metropolitan areas are identified as the sum of the administrative boundaries of municipalities, provinces, or regions. However, some scholars see specific issues with this approach, particularly the misalignment between the economic-functional boundaries and the ‘legal’ or administrative boundaries of metropolitan areas. This misalignment complicates the task of conducting a consistent comparison between metropolitan areas. In fact, the analyses of territorial dynamics typically rely on official data and statistics that are geographically associated with reference spatial units such as municipalities, regions, or other administrative areas. These, however, demonstrate significant resistance to adapting and changing in response to shifting economic, social, and demographic conditions in the territory [31]. The uncertainties arising from the disparity between official and functional boundaries become even more pronounced when urbanisation has experienced rapid growth in terms of surface area and/or population [25]. On the other hand, other research highlights anomalies and issues associated with defining functional boundaries. Indeed, while this solution may seem preferable, it can still lead to particular situations influenced by biases or political pressures. These factors can sometimes distort these boundaries, primarily through the use of non-transparent calculation algorithms or the imposition of a multitude of predetermined criteria [32]. Research and development of methodologies in this direction have already produced several but only sometimes satisfactory results. For example, a recent study conducted by Ganciu in 2023 [33] attempted to define the functional limits of a metropolis based on complex geometric modelling of the attractive forces of urban poles, again defined using the flows of commuters moving within the metropolitan area. However, although the analysis results enabled a more emphatic appreciation of the differences between the attractive forces present within a macro-region, a spatial boundary of the area of influence could not be defined with greater certainty (Figure 3 and Figure 4).

1.3. Visual Analytics for the Study and Representation of Flows in Metropolitan Areas

Other research, combining methods and technologies that exploit the potential of human visual interpretation with the increased capabilities of electronic data processing, is directed at developing procedures and algorithms for an adequate understanding of the metropolitan system being analysed than would have been possible in the past [34]. This human–machine hybridisation, referred to as visual analytics, has proven to be particularly useful for observing data from different perspectives and for different purposes using methodologies and procedures that find wide application in statistical disciplines, geographic information science, especially in the context of the research involving dynamic phenomena characterized by spatial movement [35]. In particular, in research concerning movement, visual analytics exploits and develops the legacy of classical thematic cartography, which provides various techniques for studying and representing the movements of tribes, armies, hurricanes, and more [36]. These basic cartographic techniques found their foundations between 1835 and 1855, which could be described as a “golden age” for developing thematic cartography. In fact, during this time, there was a significant surge in methodologies for representing statistical and territorial data [37]. It appears that nearly every technique currently known for representing census and geographic information, such as population numbers, income, wealth distribution, and the distribution and density of people’s movements, was invented during this period [38]. It should also be considered that the “golden age” for cartography was marked by the progression in physical and social research techniques, the beginning of the tremendous topographical surveys, and the establishment of censuses, which inevitably combined produced a fertile environment for the development of thematic cartography [39]. For example, in Victorian England, after the steam railway proved to be a practical method of communication, there was a rapid expansion of lines and branches. Thomas Drummond, Under Secretary of State for Ireland, suggested the creation of a Railway Commission to study the issue of transportation and commuting in Ireland. The Commission, in 1837, submitted a brief interim report and, in 1838, published the final document accompanied by an atlas containing maps of various kinds, including those depicting the distribution of population and the mobility of people and goods. The author of these maps was Henry Drury Harness, who had a long and distinguished career as a military and civil servant [37,40]. In particular, he prepared three maps for the final document; the first two directly concerned the Irish population, and the third contained an infographic representation of the movement of goods (Figure 5) [41]. During the same period, many other scholars, not necessarily engineers, developed other graphic techniques to apply to statistical science and spatial data representation, such as Playfair, Florence Nightingale, and Charles Joseph Minard [42]. In particular, Minard is considered by many to be a true pioneer; his innovations are recognizable for his constant search for a compromise between the demands of cartographic accuracy and the “form” with which to represent data [43]. During his work, he produced dozens of “flow maps”, depicting passenger traffic on European railways, logistics for the supply of goods and food supplies for the Paris area, and international distribution of French wines, cotton, coal, and more (Figure 6). In addition to the graphical representation of movement, Minard included numerical information, annotated or in tabular form, in his maps, which were associated with extensive descriptions of what was depicted and the conclusions that could be drawn from the analyses [44,45]. The combination of classical thematic mapping techniques with computer support has, therefore, enabled the development of electric geo-visualisations and interactive maps to explore geographic information with high user interaction, especially in research contexts characterized by information density and investigative complexity [46].

The various methodologies of visual analytics applied to movement can be categorized into four types [35]: those that observe individual trajectories, those that focus on movement variation and characteristics, those based on a bird’s-eye view where the individual movement is less important than the collective movements that, when aggregated, reveal overall spatiotemporal dynamics, and finally, those that investigate the relationship between movement and the territorial context. Some notable examples in this direction include the Chicago Area Transportation Study carried out in 1959 [47], for which a unique system, ‘the cartographatron’, was developed to visualize millions of ‘displacement lines’. The information on overall dynamics was then used to plan routes and new routes for transportation infrastructure. Another example is the electronic mapping program developed by Kern and Ruston in 1969 [48] to show geographic interactions through individual lines drawn on a mechanical-type graph plotter.

1.4. Research Objectives

The overall objective is to develop and test a methodology for identifying and measuring certain characteristics of polycentric systems to implement knowledge and an understanding of them. This methodology aims to respond, first of all, to the need to identify the boundaries of influence of the various urban centres, which has been argued to be decisive for the selection of data needed to construct indicators useful for subsequent analysis and planning.

Based on the considerations mentioned above and developing the research strand related to Visual Analytics, this study has the following objectives: (a) defining a graphic-analytical methodology for determining and graphically visualising the functional influence area of metropolises, i.e., the territorial boundary beyond which a metropolis’s attracting power no longer exerts its territorial influence; (b) defining a graphical–analytical methodology for visualising the territorial ramification of urban cores with greater attraction capacity; (c) establishing a graphical code capable of effectively visualising the functional network of metropolitan areas; also, concerning the selected case study, determining (d) the existence, number and territorial extent of macro-regions; (e) the differences between functional area of macro-regions and administrative regions.

2. Materials and Methods and Data

In this research, several methodologies traceable to the branch of Visual Analytics were tested, which, with its wealth of widely established knowledge, can be considered valuable support for addressing the combination of methods and technologies that exploit the synergy between the potential of human understanding and electronic data processing capabilities. For the previous classification, the proposed graph-analytic mix can be classified in the family of “bird’s-eye” methodologies. It is based on the algorithms of graph theory for the analytic component, which has its basis in the studies of Euler in the 18th century [49]. In contrast, the aspects related to the discipline of drawing and representation are based on the electronic evolution of some past graphical inventions invented by Henry Drury Harness and Charles Joseph Minard to map commuter flows and migrations, respectively, in the United Kingdom and France during the 19th century. In recent years, visual analysis methodologies have often been used to study human mobility, using different types of data from different sources, such as car traffic, commuting, data from smartphones and mobile telephony in general, or from social media that allow for the geographical tagging of content uploaded online. For example, traffic data in many cases comes from cameras or sensors installed along transport infrastructure, or data directly provided by public transport companies such as taxis, buses, ships, and planes [50]. When considering commuting, widely used sources include, for example, databases on entries through underground gates, which also allow the information base to be enriched with travel times and costs [51]. The ubiquity of mobile phones offers unprecedented information resources allowing each device to be located every time it is connected to a cell and movements from cell to cell [52]. Finally, social networks such as Facebook, Instagram, and even less popular ones allow us to geographically tag content that is posted online helping us to better understand people’s activities, behaviours, and mobility needs [53].

Graph theory is a branch of mathematics developed by the Swiss physicist Euler in the 18th century [49] that enables the identification and description of system elements and the description and computation of the relationships between them [54]. The discipline, as mentioned above, has found application in various research areas such as in the study of economic and social systems [55,56,57]; the study of infrastructure and transportation [58,59]; applications in urban and spatial planning [60,61,62]; and the analysis of ecological systems [63,64]. In particular, graph theory has demonstrated its adaptability for analysing commuter flows [65,66,67]. In mathematical terms, a graph “G” can be defined as a mathematical structure consisting of a non-empty set of nodes (n) denoted as V(G), a set of links (e) denoted as “E(G)”, and the relationships “Ψ” associated with each link joining two nodes:

G = {V(G); E(G); Ψ}

(1)

Using graph theory, it is possible to conceptualize the metropolis with nodes to indicate urban centres and commuter movements between nodes through links. There are different types of graphs differing in structure, relationships, connection between nodes, and other properties [68]. The graphs used to analyse the metropolitan systems in this research are geometric, weighted, and oriented. The graph is oriented because it is impossible to define equal reciprocity of commuter flows between two urban cores (i; j), in other words, commuter flow i → j and commuter flow j → i may not be equivalent, so the following relationships apply [10].

$$e_{ij}\ne e_{ji}$$

(2)

The graph is weighted because each link is associated with the number of commuters moving between two urban nodes. Finally, the graph is geometric, meaning that each node is located within an Euclidean space and is identified using an East and North coordinate pair concerning a projected spatial reference system, specifically UTM32N/WGS84. Many fundamental analyses were performed on the graphs: incoming node weighted degree (Deg_IN^w), which formally expresses the sum of all weighted links converging on each node; in other words, it allows us to calculate the total commuter flow coming from all nodes in the graph and entering daily on each node considered:

$${Deg}_{IN}^w=\sum _{j=1,n}{e}_{ij}^w$$

(3)

The calculation of Deg_IN^w makes it possible to identify urban nodes with greater commuter attractiveness. This information was later used to identify within the entire graph sub-structures called “communities”, where nodes are distributed within each cluster according to the attractiveness power exerted by each node (Figure 7).

That is, identifying a community means determining which nodes in the network are most attracted to the parent city of that community compared to all other parent cities in the network; in other words, it means determining the municipalities that gravitate within the functional area of an urban centre that has the greatest attractiveness. There are several methodologies for performing this analysis that can be classified into three families: (a) divisive methods; (b) spectral methods; and (c) methods based on optimising modularity (Q). Optimising modularity means dividing the entire network into several sub-structures where the difference between links joining nodes belonging to the same communities and links between nodes of different communities is maximum (Figure 8) [68]. The value of modularity is usually expressed as [69]:

$$Q=\frac{1}{2m}\sum \left(a_{ij}-\frac{kikj}{2m}\right)\times \partial \left(Ci,Cj\right)$$

(4)

where “k” is the degree of nodes; “m” is the number of links in the “G” graph; “aij” identifies the links in the adjacency matrix; “∂” is a parameter that takes the value 1 if nodes “i” and “j” belong to the same community; otherwise it takes value 0. The value of modularity can vary from zero to one, where 0 means poor cluster quality, while 1 means that communities are defined with high precision.

In this research, to identify communities and calculate the modularity value ‘Q’, the Louvain algorithm [70] was used. This algorithm provides relatively quick results even when analysing highly complex networks using hundreds of thousands of links. After the analytical phase, the results are provided through graphical outputs such as migration maps that represent patterns of geographic movement using arrows or bands between locations, based on information stored in ‘from-to’ tables or matrices. The areas involved in migration or other types of movement are connected by a ‘band’ or another linear graphical element, the width of which is often proportional to the magnitude of the movement [11]. To represent the territorial branching of the metropolis, as mentioned earlier, we followed the evolution of graphic techniques used in the past by Henry Drury Harness and Charles Joseph Minard. Specifically, in the procedure, applying the previous analytical method of determining macro-regions and identifying the most attractive urban cores within each of these functional areas, for each of these main urban centres, the shortest routes used by commuters departing from the secondary urban cores in the direction of the most attractive urban pole were determined. The shortest paths were determined by applying a “shortest path” search algorithm based on Edward F. Moore’s 1957 work [71]. Overlying all the shortest paths results in a tree where the nodes are generated by the intersection of the individual paths, and the weight of the link joining them expresses the total number of passengers flowing along the branch of the tree. In other words, proceeding from the ends of the tree toward the primary urban centre will result in “mother” branches whose weight is the sum of the weights of the two or more linked “child” branches. In this way, it is possible to calculate the weight of all branches of the tree and to represent all branches using different shades of colour and thickness, which are proportional to the number of commuters passing along a stretch (Figure 9).

The data used in this study were extracted from the National Commuting Matrix (NCM) and were collected during the 15th National Population Census by the National Institute of Statistics [72]. To conduct the NCM, ISTAT conducted 28,871,447 interviews to understand the daily mobility needs of the population residing in Italy and commuting daily for work, study, or access to other types of services (health, other). The questionnaire responses were processed and entered into a CSV-type continuous plot database. The ISTAT database also provided geographic information on municipal administrative units from which the relevant centroids were calculated, used as nodes in the network analyses during the analytical phase and for constructing trees in the subsequent representative phase. The geographic database of municipalities is referred to the same year as the commuting matrix to have uniformity of information. The road network, used as the basis on which to calculate the shortest commuter routes, was taken from the “Priority Layers of National Interest” project. The network was created under the State-Regions-Local Authorities Agreement on Geographic Information Systems (IntesaGIS) starting in September 2003 and was handed over by the Interregional Center, which carried out the construction management, to the Commissioning Entities in June 2005. The project represents the coverage of the road and rail routes, and hydrography and administrative limits of the national territory. The official website is not fully accessible (as of 30 July 2018), but there are still reachable files, such as one of the national ensembles. The study covered 11 Italian regions (Figure 10) and a total of 5157 municipalities, with a resident population of 33,311,161 people and a total land area of 161,091.0733 square kilometres (

Table 1. Description of the composition of the regions chosen as case studies.

Regions	Municipalities	Population	Surface Area km2
Aosta Valley	74	126,806	3262.1602
Umbria	92	884,268	8453.8895
Friuli Venice Julia	218	1,218,985	7849.359
Liguria	235	1,570,694	5419.9791
Marche	239	1,541,319	9382.4472
Tuscany	287	3,672,202	22,987.0816
Trentino Alto Adige	333	1,029,475	13,604.9236
Emilia Romagna	348	4,342,135	22,452.7705
Veneto	581	4,857,210	18,398.436
Piedmont	1206	4,363,916	25,401.3333
Lombardy	1544	9,704,151	23,878.6933
Study Area	5157	33,311,161	161,091.0733

). The most populous regions in terms of the number of people and municipalities involved in the study are Lombardy and Piedmont, where more than half of all the municipalities in the study area are located, and nearly half of the entire population considered in the research lives and commutes. The transportation infrastructure considered in this research consists of railways and roads of all grades: highways, primary and secondary roads, and municipal roads. In total, there are 213,000 km of road infrastructure and nearly 13,000 km of railways within the study area (

Table 2. Distribution of transportation infrastructure.

Region	Road (km)	Railway (km)	Road km/km2	Railway km/km2	Road km/pop	Railway km/pop
Aosta Valley	2382	94	0.730	0.0289	0.0188	0.00074
Trentino	17,510	500	1.287	0.0368	0.0170	0.00049
Piedmont	46,042	1985	1.813	0.0782	0.0106	0.00046
Umbria	8485	531	1.004	0.0629	0.0096	0.00060
Emilia-Romagna	37,062	1273	1.651	0.0567	0.0085	0.00029
Tuscany	25,272	1675	1.099	0.0729	0.0069	0.00046
Marche	8760	440	0.934	0.0470	0.0057	0.00029
Veneto	25,196	2173	1.369	0.1182	0.0052	0.00045
Liguria	7933	724	1.464	0.1337	0.0051	0.00046
Friuli-VG	6075	1476	0.774	0.1882	0.0050	0.00121
Lombardy	28,638	2066	1.199	0.0865	0.0030	0.00021

). Regions such as Piedmont and Emilia-Romagna have the highest infrastructure endowment in absolute terms. The supremacy of these two regions is also maintained by relating the kilometres of infrastructure to the regional surface area (km/km²). However, let us consider the ratio of kilometres of infrastructure to the resident population (km/inhabitant). Valle d’Aosta and Trentino Alto Adige are the regions where each resident has the highest number of kilometres of transportation infrastructure.

Morphologically, the study area is bounded to the north by the mountain range of the Alps. To the south of the mountains, the vast Po Valley mainly affects the territories of Piedmont, Lombardy, Veneto, and Emilia-Romagna. The mountain range of the Apennines, which develops according to a northwest/southeast direction, actually constitutes a natural boundary that corresponds to the administrative border between the regions of Emilia-Romagna and Tuscany (Figure 11). The evaluation and graphic processing of the morphology of the study area was developed using the Digital Elevation Model developed by the Italian Institute for Geophysics and Volcanology (INGV) with a pixel resolution of 10 m × 10 m.

3. Results

3.1. Analytical Component

Processing the commuter network reveals a highly complex relational structure. The network consists of a total of 5157 nodes interconnected by 394,465 links. Some results were expected such as the dominance of the attractive power of the most important cities in terms of economic activity and administrative power within their respective 11 administrative regions. By observing the numbers obtained through the analysis of the incoming degree of nodes (DegIN), but also the network visualisation itself (Figure 12), we understand the apparent dominance of the city of Turin in Piedmont, Milan in Lombardy, Genoa in Liguria, Venice in Veneto, Bologna in Emilia-Romagna, and finally Florence in Tuscany. As for the other administrative regions: in Valle d’Aosta, Friuli-Venezia Giulia, Trentino, Umbria, and Marche, there are undoubtedly attractive urban hubs, as can also be seen from the visual results, but their ability to dominate flows is significantly less than in the previous cases. Looking at the distribution and intensity of flows “from a bird’s eye view”, two vast polycentric metropolitan agglomerations can be clearly observed: the first one pivoting in a kind of triangle involving the cities of Turin, Genoa, and Milan, and from the latter connecting some minor nodes such as Brescia, Verona, and Padua to head up to the large node of Venice. Moreover, again from the Milan node, it is also possible to observe a second branch of the vast polycentric metropolitan area heading in a southeasterly direction towards the minor centres of Parma, Reggio Emilia, and Modena to reach the Bologna node and continue again linearly towards the Italian Adriatic belt joining the cities of Rimini, Pesaro, and Ancona. The second vast polycentric metropolitan system can be observed in the south of the Apennine Mountain range, which, as mentioned in the previous section on the description of the case study, is a natural barrier. In this case, the primary node is the city of Florence from which the westward branch branches off to join the nodes of Pisa and Livorno and a second direction parallel to the Apennines to join the nodes of Arezzo and Perugia. In summary, at first assessment, the study area appears to be characterized by two vast polycentric metropolitan systems strongly interconnected internally: the first one to the north of the Apennines encompasses the entire Po Valley and seems to extend towards the Italian Adriatic coast; the second one to the south of the Apennines, with a single central hub represented by the city of Florence, covers the entire Italian Tyrrhenian coast and likely extends much further south beyond the study area (Figure 13 and Figure 14). However, a more in-depth analysis of the network performed through community detection, as described earlier, reveals the existence of five functional macroregions, with four in the northern part of the Apennine line and one corresponding to the previous hypothesis of a vast polycentric metropolitan system mainly dominated by Florence, encompassing Tuscany and Umbria. Specifically, according to the results of community detection, the extensive polycentric metropolitan system north of the Apennines, as previously hypothesized, can be considered an aggregation of four metropolitan macroregions. Starting from the northwestern area, the first one encompasses the regions of Piedmont, Liguria, and Valle d’Aosta; the second can be roughly identified with the region of Lombardy; the third entirely includes Veneto, Trentino Alto Adige and Friuli Venezia Giulia, and the fourth is approximately composed of Emilia Romagna and Marche (Figure 15).

The results obtained regarding the existence of large polycentric systems in the Italian context seem to be generally in line with previous research carried out by Veneri [3] involving 82 Italian metropolitan areas, and then by Ganciu et al. [11], who focused on the metropolitan systems of Rome and Milan. More precisely in Veneri [3], using a functional approach, the degree of polycentricity of the metropolis is first determined and then this information is related to private transport costs and the environmental externalities produced, determining how systems with high polycentricity are the most virtuous with respect to both private costs and environmental externalities. Thus, the subsequent studies [11] for the determination of sub-centres in the metropolitan areas of Rome and Milan also determine the existence of metropolitan systems with different degrees of polycentricity due to differences in the allocation of the labour market and services that inevitably generate differences in the flow of commuters. The different degrees of polycentricity of the metropolitan systems within their respective regions can be better understood by observing the cumulative distribution of incoming commuter flows for each municipality represented in the diagrams below. For example, by means of these representations, it is possible to observe the metropolitan system of Lombardy, which is organised on a high number of municipalities with a high commuter attraction capacity with Milan obviously the main attraction pole, or Florence in the case of Tuscany. On the other hand, a lower degree of polycentricity can be observed in Liguria where the Municipality of Genoa is responsible for almost 50% of the flows of the entire Region (Figure 16 and Figure 17).

The examination of Community Detection applied to the entire study area reveals the existence of five macro-regions as already described with a high quality of cluster detection. In fact, the modularity value obtained with Luvian’s algorithm reaches a score of 0.714, which is very close to the threshold value of 1 representative of a perfect definition of the communities.

3.2. Graphic Component

The application of graphic techniques used in the past by Henry Drury Harness and Charles Joseph Minard has allowed for highlighting the territorial extent of the attractiveness of the main urban centres within their respective macroregions determined during the analytical component. Once the most attractive nodes were identified, namely Turin, Genoa, Milan, Padua, Venice, Bologna, and Florence, their respective trees were constructed by intersecting the individual paths from the commuters’ point of departure to the central city where all branches converge. The branches of Genoa and Padua were elaborated but not included to avoid excessive information overlap, which would have made the overall graphic interpretation more complex. After several attempts to choose the thickness and chromatic variation to be assigned to the importance of the branches, a satisfactory result was achieved, allowing for a more effective visual interpretation of the complex metropolitan phenomenon. For example, it is possible to observe and deduce how the cities of Milan and Turin almost entirely dominate their respective macro-regions with high intensity. In fact, one can observe how the branches with colours ranging from red to orange extend to the ends of their respective trees. Conversely, it can be observed how the cities of Bologna, as well as Venice and Florence, although they develop more extensive trees in terms of surface area and distances travelled, show a greater capacity to dominate the territory more concentrated near their “mother cities” and then significantly fade as they reach the outermost branches (Figure 18).

As already mentioned, the determination of the communities makes it possible to identify five functional macro-regions. To facilitate the understanding of a possible territorial reorganisation in addition to an obligatory mapping of the new boundaries, it no further information neededuseful to represent this result with the development of a very effective infographic such as a Sankey diagram often used to represent flows or transformations [73]. In the Figure 19, on the left-hand side are the 11 Italian regions of the study area with the respective number of municipalities, while on the right-hand side are the 5 macro-regions identified using the community detection examination, and in this case, the number indicates the number of municipalities contained. This type of visualisation makes it possible to appreciate and confirm certain characteristics of the study area; one can, in fact, observe the region of Lombardy, which presents a very solid organisational structure and is also capable of attracting municipalities belonging to Piedmont; on the contrary, in community number three, one can observe the confluence of certain regions that are less independent or with less strength of municipalities. In fact, this community is the result of almost the total union of the municipalities of the Veneto, Trentino, and Friuli VG regions.

4. Discussion and Conclusions

The connection between form, well-being, economic growth, and sustainability in polycentric metropolises has long been a subject of interest in the discipline of urban planning and beyond. Understanding the structure of urban systems and the intrinsic relationships that develop within them is a topic that is as strategic as it is complex. Research in this field is essential to support effective urban and spatial planning, capable of responding to the needs of different contexts and guiding their development. In our study, we propose a graphical–analytical methodology to determine and graphically represent the functional area of influence of metropolises and visualize the territorial ramification of urban centres with greater attractiveness. Its application in the territorial context of northern Italy made it possible to determine the existence, number, and territorial extent of macro-regions of influence and the differences between the functional area of these macro-regions and administrative boundaries. In particular, a highly polycentric and highly relational system emerged in which it was possible to distinguish macro-areas whose functional boundaries rarely coincide with regional administrative boundaries. This type of analysis can provide a beneficial cognitive basis for identifying strengths and weaknesses of polycentric urban systems, analysing balances and power relations about the factors that are underlying the formation of the directions of movement and lines of influence, such as the endowment of services, ease of access, demographic characteristics, etc., in order to provide planners with a critical reading of polycentric urban systems. At the same time, the proposed methodology allows extremely complex analyses to be represented intuitively, enabling them to be shared with a non-specialized audience.

There are some aspects that are of particular interest to the scientific community and deserve further investigation in future research, with a view to a generalisation of the methodology proposed in this research. First of all, some pre-processing processes of ‘raw’ data are heterogeneous in quality and density and therefore cannot be visualised directly [74]. Furthermore, the possibility of database errors or incompleteness must be considered, especially when research is based on open and untested data sources. Future research for a generalisation of the application should, therefore, first be directed towards determining methodologies that are less sensitive to database errors or incompleteness [75]. Furthermore, as the size of the available big data continues to grow, and with the density of information that is available, there is a need to develop synthesis solutions that allow for scalability between different levels of spatial insight and analysis.

Data visualisation is in fact a language of communication and as such it is necessary to possess the appropriate skills to be able to interpret it correctly. Unfortunately, at present, as also highlighted in an in-depth study contained within a recent Eurostat outlook report [76,77], there is a risk related to the ‘graphicacy’ skills of information consumers, indicating the level of understanding of maps, diagrams, and other visual languages [78]. This risk exists, whether there are private citizens or people with responsibility for spatial planning, differing in age, education, and culture. On the other hand, there is a widespread scientific consensus regarding the opportunities offered by human interpretation capabilities, especially in this historical period in which the availability and complexity of data are growing at an unprecedented rate [79]. In fact, considering the risks arising from low levels of graphicality, it is obvious that the main lines of investigation focus on defining the most effective ways to fully integrate human interpretive capabilities into the analytical process. Therefore, although data visualisation and human interpretation may represent a powerful tool or, better still, an opportunity if used correctly, it is also true that the language of visual communication cannot disregard a solid and effective analytical phase that precedes those of visualisation and finally interpretation.

Finally, we feel we must include further limitations associated with the proposed methodology, for example, the availability of up-to-date and timely data. Furthermore, it should be pointed out that although the analysis conducted with the aid of graph theory is valuable in describing specific aspects of commuter flows, it has limitations in its ability to provide an explanation for the motivation of these flows. This, in fact, cannot be understood solely through the representation and analysis of the relationships between nodes, since the complexity of spatial structuring is also composed of other aspects such as socio-economic, cultural, environmental, political, and other characteristics. Recognising the limitation of graph theory in offering a comprehensive explanation of a polycentric system underlines the importance of adopting an integral approach in urban planning. This suggests that planning decisions should be derived from a comprehensive and multidimensional understanding of commuting flows.

Some clarifications are also necessary on the software side; several open tools for data visualisation are currently available, such as Google Charts, Datawrapper, Baidu Echarts, Many Eyes, and Tableau, but in most cases, their application can only be considered useful if the analysis of the system is not excessively complex; on the contrary, the result that can be obtained may not be adequate in relation to the complexity of the analysis.