Markov random geometric graph, MRGG: A growth model for temporal dynamic networks

We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on Markovian latent space dynamic: consecutive points are sampled the Euclidean Sphere using an unknown kernel; and two nodes connected with probability depending function of their geodesic distance. More precisely, at each stamp-time k we add point Xk by jumping from previous one Xk−1 in direction chosen uniformly Yk length rk drawn distribution called latitude function. The connection probabilities between pair equal to envelope distance these points. provide theoretical guarantees non-parametric estimation functions. propose efficient algorithm that achieves those tasks ad-hoc Hierarchical Agglomerative Clustering approach. As product, show how MRGGs can be used detect dependence structure growing graphs solve link prediction problems.