This directory contains a set of TeX files which, when compiled into a PDF, forms the paper The Formation of Extractive Structures in Networks. This paper provides an analysis of the formation of critical node sets within a general network topology. The full paper can be found in BlockFormation.pdf.
This article develops and assesses the notions of block formation within a topological structure. We quote the abstract of the article below.
It is well-known that critical nodes or "middlemen" control information flows in a directed network and take advantage of these positions to extract excess rents from these networks. We extend this concept to critical node sets and investigate the potential contestation of these critical node sets by other node sets. This methodology allows us to introduce a game theoretic approach to analyse the formation of these critical node sets and allows the introduction of new network centrality measures that are based on potential membership of these critical node sets.
We introduce a non-cooperative game theoretic approach to network centrality based on the formation of certain critical node sets. We show that the Strong Nash equilibrium in a critical node set formation game identifies the maximally controlling critical node sets in any network. This provides a foundation to an innovative way of identifying brokerage structures in directed networks. We develop applications to the Renaissance Florentine elite network and the networks formed by the 9/11 terrorists.
The latest PDF should have already been compiled and uploaded to the repository. If the latest PDF has not been compiled, or to make changes and compile yourself, you must have a LaTeX executable installed on your system.
- For Windows I suggest using MiKTex,
- For Mac OSX I suggest using MacTeX, and
- For Ubuntu Linux I suggest using TeX Live.
All networks, and some of the analysis, were rendered with the Gephi software package which can be found here.
Please contact me with regards any issues or queries that you have.