Disassortative dynamic BA models inspired by the Bitcoin Lightning Network

The evolution of the channel graph of the Lightning Network, the main layer-2 solution on top of Bitcoin, has been often modeled as a Barabási-Albert random graph. However, the available data on the channel graph of the Lightning Network indicate that it is stabilizing over a network structure with negative assortativity, while the assortativity of a BA random graph tends to zero as the number of nodes grows to infinity.In the BA model, new edges are created when a new node joins the network and they never disappear. In the channel graph of the Lightning Network, channels can be closed by one or both of its endpoints at any time. In this paper, we propose two dynamic versions of the BA-model in which edges can disappear at any time. In the first version, the edge disappearance rate is a function of the degrees of the endpoints, in the second one it is a function of the edge capacity. Simulations show that, in both models, the assortativity converges to a negative value, that depends on the edge disappearence rate. Our results suggest that the disassortative nature of the Lightning Network, as well as that of several other real networks, could be a consequence of the dynamic nature of the edges of the network.