Generating random bigraphs with preferential attachment

TL;DR

This paper introduces an algorithm for generating random bigraphs with preferential attachment and assortative linkage patterns, enabling better simulation of complex systems like multi-agent and ubiquitous computing environments.

Contribution

It proposes a novel algorithm for creating bigraphs with controllable structural properties, filling a gap in bigraph-related modeling and simulation tools.

Findings

Analyzed graph-theoretic metrics of generated bigraphs under various configurations.

Demonstrated the algorithm's ability to produce diverse bigraph structures.

Provided insights into pattern formation in bigraph models.

Abstract

The bigraph theory is a relatively young, yet formally rigorous, mathematical framework encompassing Robin Milner's previous work on process calculi, on the one hand, and provides a generic meta-model for complex systems such as multi-agent systems, on the other. A bigraph $F = \langle F^P, F^L\rangle$ is a superposition of two independent graph structures comprising a place graph $F^P$ (i.e., a forest) and a link graph $F^L$ (i.e., a hypergraph), sharing the same node set, to express locality and communication of processes independently from each other. In this paper, we take some preparatory steps towards an algorithm for generating random bigraphs with preferential attachment feature w.r.t. $F^P$ and assortative (disassortative) linkage pattern w.r.t. $F^L$. We employ parameters allowing one to fine-tune the characteristics of the generated bigraph structures. To study the pattern formation properties of our algorithmic model, we analyze several metrics from graph theory based on artificially created bigraphs under different configurations. Bigraphs provide a quite useful and expressive semantic for process calculi for mobile and global ubiquitous computing. So far, this subject has not received attention in the bigraph-related scientific literature. However, artificial models may be particularly useful for simulation and evaluation of real-world applications in ubiquitous systems necessitating random structures.