MATHS | Graph Theory

Posted on 14/09/2013


The local newsagent is sometimes surprising when, buried in the cheap remaindered books, a completely unexpected title appears. Today, it was a book titled From Tube Maps to Neural Networks: The theory of graphs by Claudi Alsina. I’d never heard of graph theory – though it’s not surprising that such a theory exists. Graph theory is about diagrams comprised of points and lines: “The basis of graph theory is in combinatorics, and the role of “graphics” is only in visualizing things.” Given its concern with the visual, graphing is significantly one aspect of visual culture and visual communication.

Graph also refers to ‘writing’ and this indicates an intimacy and fluidity in the relationship between writing and digramming. While not a revelation, this segues into my interest in Oulipo and its engagement with mathematics and rules. Recently, I noted my interest in adopting something of George Perec’s approach in Species of Spaces to Fieldworking.

Having now googled ‘graph theory’ I’ve found another introductory text by Keijo Ruohonen which has provided further chance encounters and revelations. His text includes a chapter titled ‘Walks, Trails, Paths, Circuits, Connectivity, Components’ which seems to bear further relation to both Fieldworking and Long Time, No See? with their attention to walking and pathways. Words like route, path, walk, circuits and trail have specific meanings in graph theory …

Alsina notes the application of graphy theory in architecture, most notably explored by Christopher Alexander in Pattern Language and The Synthesis of Form. Graph theory is used to represent (or visualise) and study dynamics of cities and settlements. The way we represent many of our transport and mobility systems – as maps – is a graph: think London Underground. Alsina further says that most of our geographical maps can be interpreted as graphs and such graphs are necessary for urban analysis. Alexander’s essay, The City is not a Tree, most famously addresses this. I suspect much of our planning continues to treat the city as if it was a tree – somehow knowable and reducable to linear flows and functionality rather than complex dynamics.

Perec’s Species of Spaces also includes his essays Think/Classify and On the Art and Science of Classifying ones Books, which continue to explore disorder and disorganisation:  the futility of categorisation and the unitary. For me, this evokes the idea of the labyrinth or labyrinthine: the path, the territory and the weave are always subjective.