Fast Approximate Convex Hull Construction in Networks via Node Embedding

Geodesic convexity in networks is an intrinsic property of graphs. It aids distinguishing between real-world and random One possible application recommending new connections a collaborative network by searching for them the so-called convex hull, which minimal subgraph containing all shortest paths its nodes. However, existing algorithms constructing hulls from subsets nodes involve extensive search over subgraphs have poor scalability. Thus, they become inapplicable to large graphs such as social networks. In this paper, we propose approach fast hull construction subset on using graph embeddings. We apply well-known concept embedding space similar problem geometric learning graph, optimizing process finding induced subgraph. To preserve metric characteristics network, train neural with L1-distance loss. As result, trained model enables us approximately verify linear time, contrary previous approaches, cubic complexity.