The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing  static congestion patterns and  its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.

We consider signed networks in which connections or edges can be either positive (friendship, trust, alliance) or negative (dislike, distrust, conflict). Early literature in graph theory theorized that such networks should display "structural balance," meaning that certain configurations of positive and negative edges are favored and others are disfavored. Here we propose two measures of balance in signed networks based on the established notions of weak and strong balance, and compare their performance on a range of tasks with each other and with previously proposed measures. In particular, we ask whether real-world signed networks are significantly balanced by these measures compared to an appropriate null model, finding that indeed they are, by all the measures studied. We also test our ability to predict unknown signs in otherwise known networks by maximizing balance. In a series of cross-validation tests we find that our measures are able to predict signs substantially better than chance.

There are inherent challenges to interdisciplinary research collaboration, such as bridging cognitive gaps and balancing transaction costs with collaborative benefits. This raises the question: Does interdisciplinary research collaboration necessarily result in disciplinary diversity among collaborators? We aim to explore this question by assessing collaborative preferences in interdisciplinary research at multiple scales through the examinination of disciplinary mixing patterns at the individual, dyadic, and team level in a coauthor network from the field of artificial intelligence in education, an emerging interdisciplinary area. Our key finding is that disciplinary diversity is reflected by diverse research experiences of individual researchers rather than diversity within pairs or groups of researchers. We also examine intergroup mixing by applying a novel approach to classify the active and non-active researchers in the collaboration network based on participation in multiple teams. We find a significant difference in indicators of academic performance and experience between the clusters of active and non-active researchers, suggesting intergroup mixing as a key factor in academic success. Our results shed light on the nature of team formation in interdisciplinary research, as well as highlight the importance of interdisciplinary training.

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here, we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving substantially on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.

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