Discovery of nodal attributes through a rank-based model of network structure

The structure of many real-world networks coevolves with the attributes of individual network nodes. Thus, in empirical settings, it is often necessary to observe link structures as well as nodal attributes; however, it is sometimes the case that link structures are readily observed, whereas nodal attributes are difficult to measure. This paper investigates whether it is possible to assume a model of how networks coevolve with nodal attributes, and then apply this model to infer unobserved nodal attributes based on a known network structure. We find that it is possible to do so in the context of a previously studied "rank" model of network structure, where nodal attributes are represented by externally determined ranks. In particular, we show that node ranks may be reliably estimated by examining node degree in conjunction with the average degree of first- and higher-order neighbors.