Synthetic generation of spatial graphs

Graphs can be used to model many different types of interaction networks, for example, online social networks or animal transport networks. Several algorithms have thus been introduced to build graphs according to some predefined conditions. In this paper, we present an algorithm that generates spatial graphs with a given degree sequence. In spatial graphs, nodes are located in a space equiped with a metric. Our goal is to define a graph in such a way that the nodes and edges are positioned according to an underlying metric. More particularly, we have constructed a greedy algorithm that generates nodes proportional to an underlying probability distribution from the spatial structure, and then generates edges inversely proportional to the Euclidean distance between nodes. The algorithm first generates a graph that can be a multigraph, and then corrects multiedges. Our motivation is in data privacy for social networks, where a key problem is the ability to build synthetic graphs. These graphs need to satisfy a set of required properties (e.g., the degrees of the nodes) but also be realistic, and thus, nodes (individuals) should be located according to a spatial structure and connections should be added taking into account nearness