A physical model for efficient ranking in networks

We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each node is real-valued and varies in time as each new edge, encoding an outcome like a win or loss, raises or lowers the node's estimated strength or prestige, as is often observed in real scenarios including sequences of games, tournaments, ...

The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have recently been proposed, based on comparisons to a complete dominance graph via combinatorial and linear algebraic methods. In this paper, we review these measures and highlight some questions to which they give rise before going on to propos...

Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by the small-world property and the presence of a large number of cycles, in particular clustering. Here, we use geometric representations of undirected networks to achieve an enriched interpretation of hierarchy that integrates features defin...

Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactio...

Social networks contain implicit knowledge that can be used to infer hierarchical relations that are not explicitly present in the available data. Interaction patterns are typically affected by users' social relations. We present an approach to inferring such information that applies a link-analysis ranking algorithm at different levels of time granularity. In addition, a voting scheme is employed for obtaining the hierarchical relations. The approach is evaluated on two data...

Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general mechanisms that explain the creation and endurance of such hierarchies are not well understood. We introduce a generative model for the dynamics of hierarchies using time-varying networks in which new links are formed based on the preferences of no...

In many social networks it is a useful assumption that, regarding a given quality, an underlying hierarchy of the connected individuals exists, and that the outcome of interactions is to some extent determined by the relative positions in the hierarchy. We consider a simple and broadly applicable method of estimating individual positions in a linear hierarchy, and the corresponding uncertainties. The method relies on solving a linear system characterized by a modified Laplaci...

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases these groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (...

Link directions are essential to the functionality of networks and their prediction is helpful towards a better knowledge of directed networks from incomplete real-world data. We study the problem of predicting the directions of some links by using the existence and directions of the rest of links. We propose a solution by first ranking nodes in a specific order and then predicting each link as stemming from a lower-ranked node towards a higher-ranked one. The proposed rankin...

Rank-order relational data, in which each actor ranks the others according to some criterion, often arise from sociometric measurements of judgment (e.g., self-reported interpersonal interaction) or preference (e.g., relative liking). We propose a class of exponential-family models for rank-order relational data and derive a new class of sufficient statistics for such data, which assume no more than within-subject ordinal properties. Application of MCMC MLE to this family all...