International Specialization Dynamics

3Dominance Relationships in an Influence Graph

3.1. Introduction

Literature on influence graph properties has mainly been focused on the use of circularities (interdependencies) instead of hierarchies (dependencies; see [LAN 13]). This chapter brings together the theoretical, methodological and empirical (here, international trade over a long period) results relating to the identification and “values” of the hierarchies of an influence graph: constituent values of the measure of dependency within an exchange structure.

Let us first of all explain the concept of influence graph.

Let us consider an exchange structure in which flows from node i to node j (i,j ∈ [1, N]) are noted as x_ij ∈ From the “demand” perspective, it becomes:

where X_i is the “production” of i ^th node and Y_i is the demand from outside the structure on this node (fixed data).

Symmetrically, from the “supply” perspective:

where W_j corresponds to the “added value” of node j.

Given that X is the production column vector (X_i), Y is the external demand column vector (Y_i), and a is the matrix with the terms a_ij = x_ij/X_j (“technical coefficients;” ∀i, j: 0 ≤ a_ij ≤ 1 and From (S1) we obtain (S3):

where A = [I – a] is ...