Networks

Why Networks?

We can think of networks in fairly simple terms: imagine, for example, a network of aircraft traveling between hubs and terminals, or a network of people working together in an office. Network analysis operates under the premise that,  by looking at the structure of the network alone, we can deduce something about how the network will function, and potential information about potential nodes within the network. For example, the image below could illustrate many different kinds of networks: perhaps it is an amazon delivery network, or a social network, or an academic citation network. What is interesting is that, even without knowing anything about the kind of network it is, we can still say some things about how it is structured. The network below has some pretty big hubs - around 6 of them that are well connected to other nodes, but not strongly connected to one another. What would be the dynamics of this network if it were a social network, or a network of a company?

What might we learn from the network?

By looking at the diagram we might learn about how information or control is exerted, about which entities are isolated, and about how protracted communication channels might be. A work network in which I need to talk to my superior, who in turn talks to his boss, who in turn is one of three bosses who only talk to each other, creates very different dynamics than a network where I have connections to everyone, or where there is only one chain of command rather than three.

Network theory attempts to understand how different network structures might lead to different kinds of system performances. The field uses domain specific language - speaking of nodes, edges, degree centrality, etc. - with much of this detail falling outside of the scope of this website.

What is important is that complex systems are made up of individual entities and, accordingly, the ways in which these entities relate to one another matter in terms of how the whole is structured. Networks in complex adaptive systems are composed of individual agents, and the relationships between these agents tend to evolve in ways that lead to power law distributions between highly and weakly connected agents. This is due to the dynamics of Preferential Attachment whereby 'the rich get richer'.

At its most extreme, network theory advances the idea that relationships between objects can have primacy over the objects themselves. Here, the causal chain is flipped from considering objects or entities as being the primary causal figure that structures relationships, to instead exploring how relationships might in fact be the primary driver that act to structure objects or entities.

Generalizing Network Knowledge

In the social sciences, Systems Theory (developed by Ludwig V. Bertalanffy), was the first to endeavor to examine how networks could play a key structuring role in how a range of entities function. Systems theory positioned itself as a meta-framework that could be applied in disparate domains - including  physics, biology, and the social sciences - and it attracted a wide following. Rather than focusing upon the atomistic properties of the things that make up the system, systems theory instead attuned to the relationships that joined entities, and how these relationships were structured.

Gregory Bateson, illustrates this point nicely when he considers the notion of a  hand: he asks, what kind of entity are we looking at when considering a hand? The answer depends on one's perspective: We can say we are looking at five digits, and this is perhaps the most common answer (or four fingers and a thumb). If we look at the components of the hand in this manner, we remain focused on the nature of the parts - we might look at the properties of each finger and how these are structured. However, we can answer the question another way: instead of seeing five digits we can say that we see four relationships. Bateson's point was that the way in which the genome of an organism understands or structures the entity 'hand' is more closely aligned with the notion of relationships rather than that of digits or objects. Accordingly, if we are to better understand natural entities we should begin to examine these from the perspective of relations rather than objects.

“You have probably been taught that you have five fingers. That is, on the whole, incorrect. It is the way language subdivides things into things. Probably the biological truth is that in the growth of this thing – in your embryology, which you scarcely remember – what was important was not five, but four relations between pairs of fingers.” - Gregory Bateson

In a similar vein, Alan Turing (father of the computer!) tried to analyze the range of fur patterns that are seen on animals (spots, patches or lines), as being different manifestations of a common driving mechanism  - where shifting the timing and intensities of the relationships of the driving mechanism would result in shifts in which pattern manifests. Rather than thinking of these distinctive markings as things 'in and of themselves' Turing wanted to understand how they might simply be different manifestation of more fundamental driving relationships.

Turing based his ideas on a reaction/diffusion model showing how shifting intensities of chemical relationships could create different distinct patterns.

Networks in Complexity Theory

Network theory is important in complexity thinking because of how the structure of the network can affect the way in which emergence occurs: certain dynamics manifest in more tightly or loosely bound networks, and information, a key driver of complex processes, moves differently depending on the nature of a given network.

Small Worlds, Growth & Preferential Attachment, Boolean Networks

Key work of network theorists include that of:

• Watts & Strogatz who developed small world networks where information can move quickly across the network; 
• Albert Laszlo Barabasi who showed how networks that observe Power Laws can be generated, following the rules involving both 'growth' and 'Preferential Attachment'.
• Stuart Kauffman who developed the theory of 'boolean' networks, where any series of linked nodes will ultimately move into regular regimes or cycles of behavior over multiple iterations in time.

Philosophical Interpretations

Alongside of these more technical ways of understanding networks, the appreciation of the more fundamental role of networks in structuring reality has also gained prominence. Networks would imply that functionality is something that is distributed, non-centralized, and shifting. In the social sciences, Actor Network Theory considers how agents power can be formed through network interactions. For philosopher Gilles Deleuze, the world is composed of what he terms a Rhizomes, a concept that parallels that of a network in the sense of it being non-centralized, shifting, and entangled.

Historic Roots

The origins of network theory stretch back to earlier 'graph theory' a branch of mathematics developed by Leonard Euler, and made famous by his using graph theory to solve the "Konigsberg bridge problem". For a quick intro watch the video here:

This kind of graph analysis was considered as a relatively minor sub-field of mathematics, and only resurged when Barabasi reinvigorated the field (and transformed it into Network theory), with his network analysis work. Barabasi's work gained prominence as he was able to show how network theory could be applied to understanding the structural and functional properties of things like the world-wide-web. Today, network analysis is used in a huge array of disciplines in order to try to understand how the structure of relationships affects the functioning of a given entity - both at the level of the entire structure, and at the level of individual nodes (people, roads, websites, etc.), within the network.

Limitations?

It is perhaps worth noting that, along with computational modeling, network analysis is one of the central ways in which complexity dynamics are explored in many fields. While this kind of analysis can potentially be very helpful, the ubiquity of this strategy may have overshadowed some of its potential shortcomings. Network analysis can be very effective at demonstrating how Driving Flows can move through a system, and how Information that steers the system can be relayed, but the precise configuration of networks often has surprisingly little to do with "classic" complex systems that we observe in the natural world.

If we are interested in the dynamics that form ripples in sand dunes, roll patterns in Benard cells, murmurations of starlings or even the emergence of ordered entities in Conway's Game of Life, then network structures do not appear to be playing any particular role. It is not as though graphing relationships between individual grains of sand on a dune will help us unravel the dynamics that form the emergent ripples. While network analysis often tries to pinpoint distinct actors in a system, very often agents in a complex system do not behave in distinctive ways. It is therefore somewhat surprising that Network Analysis has garnered so much strength as a key tool in complex systems research. Again, this is not to say that networks do not matter - certainly there are certain features of complex systems like the internet have key nodes like "wikipedia" that once entrenched help steer the system dynamics. It is just that there are many other features of complexity dynamics that may be overlooked if our primary focus is only on network relationships in a system.

Back to Core Concepts

Back to Navigating Complexity