A scalable directed graph model with reciprocal edges

A stronger relation exists between two nodes when they each point to one another (reciprocal edge) as compared to when only one points to the other (one-way edge). The proportion of reciprocal edges in a network is a good indicator of how tight the relations among the nodes are. The mutual relations could be an indication of friendship in a graph with social behavior or the information flow in a communication network. Despite their importance, reciprocal edges have been disregarded by most directed graph models. In our study, we propose a directed graph model that (i) combines the correct proportions of both reciprocal and one-way edges, (ii) matches the in-, out-, and reciprocal-degree distributions of the fitted graph, and (iii) requires only O(m) work for a graph with m edges, making it scalable to very large graphs. We show the effectiveness of the proposed model on several real-world graphs and compare it to other state-of-the-art models