Complex Systems Are Not Networks; They are Cases.

Let me be clear right from the 'get go' of this post!  I am a huge fan of network science!

I regularly teach the stuff in my college courses; I do network research myself; and my colleagues and I have incorporated adjacency matrices and relational data into our development of our novel approach to case-based modeling.  In fact, in my humble opinion, network science is probably one of the most important intellectual triumphs of science in the last twenty years!  

So, there!  I think my opening point is well made: in the vernacular of the 1970s, network science rocks!

Still, it is not everything!  What?

Let me explain.  See, it really hit me the other day.  I was thinking about the case, right?

More specifically, I was thinking about David Byrne's case-based-complexity-science notion that cases are complex dynamical systems c_i (j), where j denotes the time instant t_j.

I was also thinking about case-based modeling, the version of case-based method that my colleagues and I have developed, which (pace Byrne) treats complex systems as a set of cases, each its own complex dynamical system.

So, what is key to both views?  It is this idea that cases are these complex things,  In fact, in our work, they are so complex that we treat cases as k dimensional row vectors (c_i = [x_i1,...,x_ik]) comprised of a set of measurements—which, usually, given our health science focus, constitutes some combination of clinical, compositional or contextual variables.

So, what does all this have to do with networks?

Well, actually, a lot.  See, an obvious point just sort of suddenly hit me.  But, as with many things in life, sometimes the obvious can go unnoticed.

Put simply: 

1. Cases are more than nodes in some adjacency matrix.  Said another way, there is more to a case than its position within a network or the relationships it shares with other nodes. Cases are complex, comprised of characteristics (measurements) that are beyond (cannot be reduced to) the relational.  

2. In turn, therefore, complex systems cannot be reduced to (or studied solely as) networks, as the agents of which these systems are comprised are not just nodes or positions within some network.  In other words, because network science only studies cases as nodes, it does not constitute the robust model of complex systems it is generally touted to be.  Network science maps only one particular dimension (the relational) of the complex systems it studies.

Now, don't get me wrong.  I know that just about anyone is network science would respond to my insight with the retort, "No duh!"  So, I am not trying to construct a straw-person here.

What then, exactly, am I constructing?

I am constructing a caveat to network science and, more broadly, the complex sciences, that I think worth a few moments thought.

I read an interview, recently, with the noted physicist, eco-systems theorist and complexity scientist, Fritjof Capra--click here to read interview.  

Capra is the author of one of my all-time favorite books, The Web of Life, and is a major advocate of networks as one of the key patterns of life.  In fact, the point of the interview was to discuss Capra's views on the utility of networks for understanding complexity.  In fact, the title of the article is Networks as a Unifying Pattern of Life Involving Different Processes at Different Levels. 

However, in his opening argument, Capra makes the following point.  He basically argues that, while studying networks as patterns of organization is necessary, is in insufficient; the nodes, as cases, need to be understood.  This is particularly true of social networks, where the nodes help us understand deeper aspects of a complex system, including such things as meaning, symbolic interaction, culture, politics, the complexity of the people the nodes represent, and so forth.  He states:

Although I can observe a network pattern, I cannot really understand it if I don't know what an enzyme is, and how it interconnects various processes as a catalyst. Similarly, in a human community the network pattern is a pattern of communications. It interconnects individual processes of communication that create ideas, information and meaning. So, we need to address the question of meaning in terms of social science, political science, anthropology, philosophy, history and so on. The social sciences and the humanities have to be drawn in to deal with the level of meaning. Only then will we really understand what's going on in a community. We can draw diagrams, and people do that. They say, person A has 4 connections in a company and person B has 6 connections; they draw little stick figures and show how they are connected to other stick figures. But to me, it does not mean much because they don't deal with the dimensions of meaning, of culture, of consciousness. So, to come back to the original issue, a unified theory is unified only through the patterns of organization [networks], but it's not a complete theory. I don't even call it a theory, I call it a unified view of life, mind and society. And it's the pattern of organization, the formal aspect, that interconnects the different domains, but the content and the nature of the processes are different in each domain. 

So, following Capra, my caveat is simple: 

remember that nodes are not just nodes; they are cases!  As such, complex systems are not networks; complex systems are sets of cases.