Solvable Metric Growing Networks

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen to be embedded in a metric arrangement, where the geographic distance between vertices plays a crucial role. The present work proposes a model for growing network that takes into account the geographic distance between vertices: the probability that they are connected is higher if they are located nearer than farther. In this framework, the mean degree of vertices, degree distribution and shortest path length between two randomly chosen vertices are analysed.