Network Topology Inference

Network graphs are constructed in all sorts of ways and to varying levels of completeness. In some settings, there is little if any uncertainty in assessing whether or not an edge exists between two vertices and we can exhaustively assess incidence between vertex pairs. For example, in examining one’s own network of Facebook friends, the presence or absence of an edge can be assessed through direct inspection. In other settings, however, constructing a network graph is not so straightforward. We may have information only on the status of some of the potential edges in the network, but not all. Alternatively, we may not even have the ability to directly assess whether or not an edge is present. Rather, it may be that we can only measure vertex or edge attributes that are to some extent predictive of edge status. In such cases, it can be natural to consider the task of constructing a network graph representation from the available data as one of statistical inference.