Large-scale measurement of aggregate human colocation patterns for epidemiological modeling.

To understand and model public health emergencies, epidemiologists need data that describes how humans are moving and interacting across physical space. Such data has traditionally been difficult for researchers to obtain with the temporal resolution and geographic breadth that is needed to study, for example, a global pandemic. This paper describes Colocation Maps, which are spatial network datasets that have been developed within Meta's Data For Good program.

Percolation on sparse networks.

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate percolation as a message passing process and demonstrate how the resulting equations can be used to calculate, among other things, the size of the percolating cluster and the average cluster size. The calculations are exact for sparse networks when the number of short loops in the network is small, but even on networks with many short loops we find them to be highly accurate when compared with direct numerical simulations.

Coauthorship and citation patterns in the Physical Review.

A large number of published studies have examined the properties of either networks of citation among scientific papers or networks of coauthorship among scientists. Here we study an extensive data set covering more than a century of physics papers published in the Physical Review, which allows us to construct both citation and coauthorship networks for the same set of papers. We analyze these networks to gain insight into temporal changes in citation and collaboration over the long time period of the data, as well as correlations and interactions between the two.

Competing epidemics on complex networks.

Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease.

Efficient and principled method for detecting communities in networks.

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times.

Stochastic blockmodels and community structure in networks.

Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world networks, which typically display broad degree distributions that can significantly affect the results. Here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks.

Random graphs containing arbitrary distributions of subgraphs.

Traditional random graph models of networks generate networks that are locally treelike, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly nontreelike neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a class of random graph models that incorporates general subgraphs, allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties.

Message passing approach for general epidemic models.

In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for transmission and recovery. Time intervals for real diseases, however, have distributions that in most cases are far from exponential, which leads to disagreements, both qualitative and quantitative, with the models. In this paper, we study a generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times.

Random graph models for directed acyclic networks.

We study random graph models for directed acyclic graphs, a class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models roughly analogous to the fixed edge number and fixed edge probability variants of traditional undirected random graphs. We calculate a number of properties of these models, including particularly the probability of connection between a given pair of vertices, and compare the results with real-world acyclic network data finding that theory and measurements agree surprisingly well-far better than the often poor agreement of other random graph models with their corresponding real-world networks.

Random acyclic networks.

Directed acyclic graphs make up a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the model's properties, including connection probabilities and component sizes, as well as a fast algorithm for simulating the model on a computer. We compare the predictions of the model to a real-world network of citations between physics papers and find surprisingly good agreement, suggesting that the structure of the real network may be quite well described by the random graph.

Robustness of community structure in networks.

The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is statistically significant or whether, conversely, it could have arisen purely as a result of chance. In this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure.