Frontiers of Design Science: The Network City

Cities rich in connections are more economically productive.

Traditional London street showing the complex network of connections between public and private spaces — connections of movement, sight, sound, and smell. These connections are able to be controlled and modulated by the users of the spaces (with doors, windows, gates, blinds, etc).

Image by Michael Mehaffy

“Only connect,” the writer E. M. Forster said famously — and modern scientists working with network structures are learning how right he was. Forster was talking about how to tell a good story, but it turns out that the same principles for creating richly interconnected structures do apply to making good cities, or other good designs. And what’s all the more interesting (and important) is how bad we’ve gotten at this in recent years — and why that came to pass. Jane Jacobs, the great urbanist and economist, put these ideas to intelligent use in her observation of what made cities such evident crucibles of economic productivity. It was proximities, she said, and networks of proximity, that allowed people to exchange knowledge and creative activities. These “Jacobs spillovers” are a major subject of research in economic science today. Something similar seems to help explain why cities are such resource-efficient places too. Just as cities promote “knowledge spillovers,” they seem to promote “resource spillovers” too, where the waste of one process (say, heat from an energy plant) can become the input of another (say, to heat a building). But these efficiencies can only happen if there is a pattern of proximity, and the possibility of inter-connection. Cities, Jacobs realized, are webs of connectivity, between people, activities, and places. And these webs were all rooted in the connective pattern of the public realm — the street and the sidewalk. Not only did this public realm allow the creation of networks of connection on the physical scale of human beings and their movements, it also allowed users to control the degree of connections, and to disconnect and reconnect where they needed to.

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If I’m sitting on the stoop of my house, I can become more connected to the people outside by walking out to the street — or I can walk back into my house and shut the door. I can draw the blinds, or open the window, or go out on my balcony, or make lots of other “modulations” to my degree of connection. What this means is that my neighbors and I can change the pattern of connectivity of our street and our neighborhood from the bottom-up, not waiting for planners or developers to come in and do it. We can “self-organize” as a neighborhood. This capacity of self-organization in networks turns out to be extremely important in living systems. We argue that it is just as important for cities. Network theorists now tell us that only certain kinds of networks can self-organize. These networks form better patterns of relationships by reconnecting — in a sense, they are capable of “learning”, not unlike the way the neural networks of the brain learn through changing the relative intensity of their neurons’ synapses.


A city is composed of overlapping, connected, evolving networks that tie together nodes and events on different physical and temporal scales.

Figure by Nikos Salingaros

Urban networks can develop into what are known as “small-world” networks. In a small-world network one node is linked to all the other nodes through only a few steps, yet the total number of connections is extremely efficient and “parsimonious”. These special nodes are catalysts for establishing connections. It’s a bit like when you meet someone and you find that you have a common acquaintance, and you say: “you know them? Small world!” In a sense it is a small world, when people like your friend are around, because they serve as special connectors between lots of other people. Places play that role too — but only if they are connected in the right way to other places. There are many examples of places that do this well, and these are places that, lo and behold, are often fun to be in. Thriving neighborhood streets, bustling downtowns, great old cities — they all contain these network patterns in abundance. These patterns are not deterministic: they recommend and encourage connections to form, which can grow and change over time. But many urban patterns used extensively since World War II do not allow spontaneous connectivity. Nowhere is this easier to see than in the fragmented patterns of contemporary “sprawl”. There is a correlation here, and not a simple coincidence. For it seems we deliberately planned this very inefficient kind of network structure, because we mistakenly thought it was more efficient. It was only efficient in certain limited ways — especially those that made things easier for planners! As we discuss in our book Principles of Urban Structure (2005), the phenomenon of an “autocatalytic set” — a kind of network originally observed in evolutionary biology — also applies to cities. A city comes alive only when it is a network that connects many different types of urban activities and nodes. Just as in a primordial mix of organic chemicals that somehow gave rise to the first living forms, you need a tremendous variety of different components for this to happen. And you also need catalysts to speed up reactions that would otherwise take too long to be useful. Since we cannot expect that catalysts just happened to be found where they were needed, it’s more likely that every different chemical acts as a catalyst for some pair of other chemicals to combine. In the urban analogy, every element present acts as a catalyst for the other elements to connect.


Mutual catalysis: all elements interact, while also acting as catalysts for each other. For example, B acts as a catalyst for elements C and D yet B also interacts with A, helped by catalyst C.

Figure by Nikos Salingaros

This means that the traditional, mixed-use city is alive, precisely because of its inclusivity of distinct functions, different scales, and different dynamics — which holds as long as one of them doesn’t destroy the others. Every diverse place and function should catalyze other essential urban functions, and this is what keeps the network connected and keeps its flows going. It is true that many urban functions are antagonistic, yet in the best situations they reach some accommodation, and maintain a dynamic balance (what is called “homeostasis”). Just as in an ecosystem, the predator eats the prey, yet both balance each other, and if one of them disappears, the other one is likely to be in trouble. Most people think that urban sprawl is an unhealthy form of urban growth. In fact, its negative effects are now well-documented: it consumes resources at a far faster rate per person than more compact and pedestrian-interconnected developments, and it takes a serious toll on human wellbeing. We now see, in the wake of the mortgage default calamity, that sprawl is likely to exact an unbearable cost to our long-term economic health. But the essential problem with sprawl is not only low density. Nor is it only homogeneity of function. Instead, sprawl is a pattern of connectivity — of the way streets connect or don’t, the way different uses connect or don’t, the way pedestrian paths connect or don’t. These can be mapped as network patterns, and we can learn a lot from those maps. To achieve the auto-catalytic set necessary for a living city, sprawl, because of its stretched and fragmented network geometry, requires enormous expenditures of energy: it is, in fact, the most energivorous urban invention in history.


A set of urban nodes looks neatly grouped on plan — but the connectivity is so badly designed that one has to go all the way around to get to an adjacent building.

Figure by Nikos Salingaros

One kind of common connection system is what is known to mathematicians as a “tree”. Transportation engineers have used this graph structure in street systems, in what is called the Functional Classification System. It looks a lot like a tree — there is a big “trunk” (the arterial); smaller “branches” (the collector roads); and finally the “twigs” (the local streets). This is how many suburban developments were deliberately structured. Notice that the parts don’t interconnect via multiple paths, and especially that the most convenient paths are missing. Once you are at one twig, you can’t get across to another twig unless you go all the way up to a branch, or even to the trunk and get back down again. This is an important restriction on the connectivity of the network — as Christopher Alexander noted in his famous 1965 paper “A City is Not a Tree”. By contrast, as Alexander pointed out, most of our older cities used a multiply-connected network that is not a hierarchical “tree”. You could move around the urban web in many different ways, and you could get to your destination more easily. Along the way, you would have opportunities to encounter many more people, and over time, form relationships with them, and build what is known as “social capital”. This is the stuff of which communities are made. Given this framework of proximities, other kinds of activities can also take place on this interconnected pattern of the urban web, including flows of people, knowledge, materials, and energy. Here is where we begin to see what Jane Jacobs was getting at with “Jacobs spillovers” — and our own more recent work with “resource spillovers”. The city creates a kind of “metabolism,” a network in which knowledge and resources cycle from one system to the next, and in which the output of one system, the “waste,” becomes the input of another — and so on and so on. A characteristic of efficient, living networks is that they obey a fractal distribution, known as an “inverse-power law.” That is, the network branches into smaller and smaller pathways, which become more and more numerous. This phenomenon leads to redundancy, which is surprisingly the basis for resiliency of the entire system. The network is much more resilient if its flows, normally along primary channels, can be distributed into secondary and even tertiary channels when the need arises. Modernist architectures and cities fail on this account, being designed for maximum flow efficiency but minimal resiliency. That’s because they favor larger scales rather than smaller scales: by concentrating on big things like highways and removing intermediate and smaller scales such as sidewalks and pedestrian paths. When planners design our cities to maximize flow, treating human beings as unemotional and supposedly “rational” urban components, all the qualities worth living for are neglected. And so are the ties to sustainability. The critical mechanism of “fractal loading”, linking events on different spatial and temporal scales, is undone by linearization. Somebody decides on the network structure, based upon narrow criteria — and gets everything wrong!


Fractal loading adds information at smaller scales and events onto primary channels, creating a rich and efficient transport mechanism.

Figure by Nikos Salingaros

A living city’s distinct yet connected, interacting, competing, dynamic networks all function on different scales. Where those networks meet is where life occurs. Here, the physical structure influences urban life for better or worse, because it’s here at the crossovers that human activity is most vulnerable. In a city, the human scale is where information exchange occurs, where our surroundings nourish us with joy and wellbeing, fulfilling our emotional needs. It’s at this level that biophilia becomes an important nourishing effect. Think of the analogy with the blood flow network trickling down to capillaries — we no longer talk of “flow” but instead of “diffusion”. Computed/evolved urban form looks irreducibly complex — the result of networks cooperating with the physical geometry. If we aren’t careful, we will try to stuff the web of tissue-like connections of a living city into simple, neat categories — and we will cut it to pieces.


Where two distinct types of network meet, flow slows down to diffusion. This is where the network structure is most vulnerable — and interestingly, where living processes occur.

Figure by Nikos Salingaros

Let’s think of built urban structure and infrastructure as a city’s “hardware” — a matrix that can be changed only after considerable time and expense. The “software” is what can move around, connect, exchange information, etc. In a nutshell, as long as we have access to unlimited resources of energy and supporting resources, we can make a city with poor “hardware” run by pushing the network connectivity burden onto the “software”. But, as computer designers know only too well, using poorly-designed hardware with increasingly complex software is asking for trouble — it is only a matter of time before the system becomes unmanageable. The remedy is known and is standard practice by now in the design of complex computer systems: maintain a balance between the hardware and the software complexities. And most important of all, as functions evolve, make sure an imbalance doesn’t build up. Therefore, when the oil runs out, and the climate goes haywire, what will we do then? We may well come to regret that we didn’t pay more attention to the structure of our networks — especially, the structure of efficient, livable, walkable cities.

Michael Mehaffy is an urbanist and critical thinker in complexity and the built environment. He is a practicing planner and builder, and is known for his many projects as well as his writings. He has been a close associate of the architect and software pioneer Christopher Alexander. Currently he is a Sir David Anderson Fellow at the University of Strathclyde in Glasgow, a Visiting Faculty Associate at Arizona State University; a Research Associate with the Center for Environmental Structure, Chris Alexander’s research center founded in 1967; and a strategic consultant on international projects, currently in Europe, North America and South America.

Nikos A. Salingaros is a mathematician and polymath known for his work on urban theory, architectural theory, complexity theory, and design philosophy. He has been a close collaborator of the architect and computer software pioneer Christopher Alexander. Salingaros published substantive research on Algebras, Mathematical Physics, Electromagnetic Fields, and Thermonuclear Fusion before turning his attention to Architecture and Urbanism. He still is Professor of Mathematics at the University of Texas at San Antonio and is also on the Architecture faculties of universities in Italy, Mexico, and The Netherlands.

Read more posts from Michael and Nikos here.

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