Lightning Network Economics: Topology

By design, the Bitcoin protocol has a low throughput. The Lightning Network (LN) is a layer-two solution built to increase throughput by cryptographically securing commitments to transactions and only occasionally converting cumulative balances into on-chain transactions. LN channels enable payments between nodes connected by a path of channels. The payment flow through a channel determines its cost. Different channel topologies can support the same underlying flows but impose different costs. This paper obtains necessary conditions for cost-minimizing topologies by identifying local costreducing strategies. The first local strategy entails repositioning of channels. The second entails adding hubs to handle the flows of groups of nodes. The paper also evaluates the efficiency of a global configuration, obtaining bounds on the minimum cost topology and showing the unusual circumstances in which the cost minimal structure is a hub that connects to all other nodes.