Sven Fischer

By Steve Peters and Karen Stephenson

In this addendum, which was the basis for an article published at the network conference 2021, we discuss a mathematical description of a network field. We describe the exchange of capital between objects in a team which we call a network. We make the assumption that exchanging capital between the actors in the field is the same as exchanging kinetic and potential energy. In our model, we use three types of capital: financial, human, and social to represent the qualifications of an object. By analogy, a non-relativistic gravitational field can be described by a time dependent Kinetic Energy part minus a position-dependent Potential Energy part. Here we describe a non-relativistic network field as Lagrangian with a time-dependent Financial Capital part minus a relative position-dependent Potential energy part. The description of the network field and especially the potential energy for a certain area in the field is comparable to the description of a Graph Neural Network for a set of nodes, a concept from deep learning theory. We use the Graph Neural Network to analyze the effects of exchanging potential energy in a network. We also use it to calculate the optimum distribution of qualifications of the actors in a team.

Part of the book: Toward a General Theory of Organizing