Large Scale Systems and SIR Models: A Featured Graphon Approach

Modelling large networks is impractical since the difficulty of computation increases combinatorically with every node added. One approach to alleviating these issues is to find a limit object of a corresponding graph sequence called a graphon, which is associated with a limiting adjacency matrix mapped to the unit square. However, graphons can be difficult to use computationally. To this end, a type of random graph called a featured graph is introduced, which is a graph sequence with meaningful vertex attributes. Following this, the convergence of the adjacency matrix as an operator to the featured graphon limit is explored. Convergence is qualitatively demonstrated on an SIR epidemic model generalized to multiple communities.