Networktheory

25Sep15

If there is one metaphor which has been dominant in the past decade as a way to understand our world it has been ‘the network’. The network as a universal explanans has probably been on the rise since the advent of the internet. Nowadays, everything is a network: we think trough neural networks, we act in social networks, we live in the network society, we communicate through computer networks, we work in network organizations, we network to find new business opportunities, we understand the world through network analyses and actor-network-theory – and so on. Does understanding the world as a network really bring so much intellectual prosperity, or is it just an intoxicating meme that blurs our vision and distracts us from pursuing more important matters? This is the first in a short series of posts analyzing the network as a metaphor and as a theory. Within this series I will try to expose some of the underlying conceptual and –sometimes- ideological luggage which the network  – as a metaphor and theory –  carries.  In this first episode I will lay down some fundamental concepts of mathematical network theory and discuss their implications on theory formation.

One good thing about network theory is, most probably, that it can be built on mathematical foundations. Let me discuss some of this mathematical network theory. Mathematicians see networks as collections of connected points. The points are called the nodes of the network, the connections are called the edges. All connected things can be described in terms of edges and nodes. A classic problem in network theory, for example, has been the riddle of the bridges of Köningsberg, shown below. The question was ‘can a person walk all the bridges of Köningsberg once and only once’?

network

As Leonard Euler showed, network theory is well suited to solve this problem. A book like “Nets, Puzzels and Postmen” will give you a neat introduction to the problem and it will tell you why the answer is no. For this brief introduction, however, it is enough to understand that the shores in this picture (A,B,C and D) are nodes and the bridges in between them (a,b,c,d,e,f,g) are edges. To understand a network we must know what the edges and nodes are, but, the Köningsberg problem is really about the bridges, not the shores. More in general, network problems typically deal with the edges: they are about the connectivity, not the things which are connected as such.

Most colloquial network explanations share this emphasis on the connectivity with the mathematical version. When we explain a riot with network theory, we focus on how vandals connect and communicate, not on the motives of the individual vandals. We do not analyze the leaders, their motives and the reasons for using violence, but we focus on how they maintain their leadership through the connections they form with others. A network analysis of the black liberation movement in the America of the 1950ies, would not focus on Rosa Parks or Martin Luther King as individuals, but on the role of churches in spreading their ideas. Similarly, the ‘Arab Spring’ is analyzed for the role of social media in the revolt but not for the underlying social changes and policies that influence the event. New and exciting as these explanations may be, typical network explanations are almost by definition somewhat ephemeral and this quality can be an impoverishment compared to other explanations. Is the question whether a Köningsberger can walk all bridges once and only once really more important than the question why they would want to walk to the other side at all? Often not.

This focus on the ‘in between’ may be an advantage of network theory and it may be refreshing, in particular in social science, in which the particulars of the individual who exerts his influence may have received a little too much attention in the past. However, discarding the individuals alltogether and focusing on the network alone seems like a bad idea too. In the end we need well connected, remarkable individuals.

Reading more.

This post is part of a series. In my next post I will ask to what extent network explanations are really an improvement to other kinds of explanations. The third post will deal with digital networks, as a paceholder for ‘real’ networks. And the fourth post will deal with centralized and decentralized control in networks.

I wrote about the importance of metaphor in my post “Reasoning on Metaphorical Foundations”. I discussed several applications of network theory to marketing in my posts “Modeling the connected customer” and “The Traveling Influence Problem”.

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