Expanded Borel Cayley Graphs (Ex-BCGs): A novel communication topology for multi-agent systems

In our early work, we reported Borel Cayley Graphs (BCGs) have the best topological and graph-spectral properties compared to toroidal and diagonal mesh networks and small-world networks. However, BCGs' dependence on generating parameters in size selection and network characteristics has been a challenge in network applications. In this paper, we propose Expanded Borel Cayley Graphs (Ex-BCGs) as a communication topology for multi-agent systems. Ex-BCGs are group-theoretically expanded graphs from BCGs with fixed generating parameters. Ex-BCGs not only conserve constant nodal degree and node labeling scheme but also inherit the communication efficiency of the original BCGs. With experimental results, we show the proposed Ex-BCGs no longer require new generating parameters for new sizes. Moreover, we show resolution of this constraint to produce efficient topological and graph-spectral properties and fast convergence speed when compared to BCGs of similar sizes. We also present the Cut-Through Rewiring (CTR) algorithm as a fault-tolerant methodology against node-failures by regarding pruning nodes as node-failures and utilizing the CTR as a way of recovering connections for neighbors of the pruned nodes in multi-agent systems. The numerical results show that resized networks from Ex-BCGs by the CTR algorithm are more fault-tolerant with robust connectivity, efficient topological properties and faster convergence speed than BCGs.