20, Towards a Graph Calculus for Decentralized Social Networks

Open Risk White Paper 20: Connecting the Dots: Towards a Graph Calculus for Decentralized Social Networks

We develop graph representations of decentralized (heterogeneous) Social Web networks. We build primarily on the machinery of multilayer networks with their associated tensor representations.

We expand on the specialized subclass of so-called layer-disjoint networks as they offer powerful tools for modeling complex online interactions of Actors within distinct Communities. We focus on the quantitative metrics and tools that can be expressed using such a framework, starting with basic building blocks and establishing the practical correspondence between adjacency tensors and supra-adjacency matrices, culminating with a discussion of the construction and use of tensor graph Laplacians.

These tools can on the one hand help ex-post empirical (statistical) work in analyzing the characteristics of current decentralized networks, on the other hand they enable ex-ante simulation and quantification of heterogeneous network properties and behavior.

Download

OpenRiskWP20_010926 PDF

Citation

@ARTICLE{OpenRiskWhitePaper20,
 author = {P. Papadopoulos},
 year = {2026},
 note = {\href{https://www.openriskmanagement.com/post-media/2026/09/OpenRiskWP20_010926.pdf}{Download URL}},
 title = {{Open Risk WP20: Connecting the Dots: Towards a Graph Calculus for Decentralized Social Networks}},
 journal = {Open Risk White Papers}
}