Controlling reciprocity in binary and weighted networks: A novel density-conserving approach

We introduce efficient Network Reciprocity Control (NRC) algorithms for steering the degree of asymmetry and reciprocity in binary and weighted networks while preserving fundamental network properties. Our methods maintain edge density in binary networks and cumulative edge weight in weighted graphs. We test these algorithms on synthetic benchmark networks, including random, small-world, and modular structures, as well as brain connectivity maps (connectomes) from various species. We demonstrate how adjusting the asymmetry-reciprocity balance under edge density and total-weight constraints influences key network features, including spectral properties, degree distributions, community structure, clustering, and path lengths. Additionally, we present a case study on the computational implications of graded reciprocity by solving a memory task within the reservoir computing framework. Furthermore, we establish the scalability of the NRC algorithms by applying them to networks of increasing size. These approaches enable a systematic investigation of the relationship between directional asymmetry and network topology, with potential applications in computational and network sciences, social network analysis, and other fields studying complex network systems where the directionality of connections is essential.