The simpliciality of higher-order networks.

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific entities participate in an interaction, and subsets of those entities also interact with each other. Traditional modeling approaches to higher-order networks tend to either not consider inclusion at all (e.

Reconstructing networks from simple and complex contagions.

Network scientists often use complex dynamic processes to describe network contagions, but tools for fitting contagion models typically assume simple dynamics. Here, we address this gap by developing a nonparametric method to reconstruct a network and dynamics from a series of node states, using a model that breaks the dichotomy between simple pairwise and complex neighborhood-based contagions. We then show that a network is more easily reconstructed when observed through the lens of complex contagions if it is dense or the dynamic saturates, and that simple contagions are better otherwise.

Network compression with configuration models and the minimum description length.

Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by their degree distribution and is foundational to many areas of network science. However, configuration models and their variants are often selected based on intuition or mathematical and computational simplicity rather than on statistical evidence.

Hypergraph reconstruction from uncertain pairwise observations.

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here, using Bayesian inference, we investigate the general problem of reconstructing a network in which higher-order interactions are also present.

Accurately summarizing an outbreak using epidemiological models takes time.

Recent outbreaks of Mpox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The feasibility of this estimation task is known as the practical identifiability (PI) problem. Here, we investigate the PI of eight commonly reported statistics of the classic susceptible-infectious-recovered model using a new measure that shows how much a researcher can expect to learn in a model-based Bayesian analysis of prevalence data.

Opposing Responses to Scarcity Emerge from Functionally Unique Sociality Drivers.

AbstractFrom biofilms to whale pods, organisms across taxa live in groups, thereby accruing numerous diverse benefits of sociality. All social organisms, however, pay the inherent cost of increased resource competition. One expects that when resources become scarce, this cost will increase, causing group sizes to decrease.

Spatial epidemiology and adaptive targeted sampling to manage the Chagas disease vector Triatoma dimidiata.

Widespread application of insecticide remains the primary form of control for Chagas disease in Central America, despite only temporarily reducing domestic levels of the endemic vector Triatoma dimidiata and having little long-term impact. Recently, an approach emphasizing community feedback and housing improvements has been shown to yield lasting results. However, the additional resources and personnel required by such an intervention likely hinders its widespread adoption.

Clustering of heterogeneous populations of networks.

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might be different on weekdays and weekends, for instance.

Reconstruction of plant-pollinator networks from observational data.

Empirical measurements of ecological networks such as food webs and mutualistic networks are often rich in structure but also noisy and error-prone, particularly for rare species for which observations are sparse. Focusing on the case of plant-pollinator networks, we here describe a Bayesian statistical technique that allows us to make accurate estimates of network structure and ecological metrics from such noisy observational data. Our method yields not only estimates of these quantities, but also estimates of their statistical errors, paving the way for principled statistical analyses of ecological variables and outcomes.

A clarified typology of core-periphery structure in networks.

Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often applied interchangeably despite the fact that they can yield inconsistent descriptions of core-periphery structure. For example, two of the most widely used algorithms, the -cores decomposition and the classic two-block model of Borgatti and Everett, extract fundamentally different structures: The latter partitions a network into a binary hub-and-spoke layout, while the former divides it into a layered hierarchy.

Inference, Model Selection, and the Combinatorics of Growing Trees.

One can often make inferences about a growing network from its current state alone. For example, it is generally possible to determine how a network changed over time or pick among plausible mechanisms explaining its growth. In practice, however, the extent to which such problems can be solved is limited by existing techniques, which are often inexact, inefficient, or both.

Improved mutual information measure for clustering, classification, and community detection.

The information theoretic measure known as mutual information is widely used as a way to quantify the similarity of two different labelings or divisions of the same set of objects, such as arises, for instance, in clustering and classification problems in machine learning or community detection problems in network science. Here we argue that the standard mutual information, as commonly defined, omits a crucial term which can become large under real-world conditions, producing results that can be substantially in error. We derive an expression for this missing term and hence write a corrected mutual information that gives accurate results even in cases where the standard measure fails.

Macroscopic patterns of interacting contagions are indistinguishable from social reinforcement.

From fake news to innovative technologies, many contagions spread as complex contagions via a process of social reinforcement, where multiple exposures are distinct from prolonged exposure to a single source. Contrarily, biological agents such as Ebola or measles are typically thought to spread as simple contagions. Here, we demonstrate that these different spreading mechanisms can have indistinguishable population-level dynamics once multiple contagions interact.

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm.

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require or even operations per update-where is the number of nodes-display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous.

Exact analytical solution of irreversible binary dynamics on networks.

In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), and nodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfy a predetermined condition. We introduce a set of recursive equations to compute the probability of reaching any final state, given an initial state, and a specification of the transition probability function of each node. Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, we also introduce an accelerated algorithm, built around a breath-first search procedure.

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks.

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation.

Construction of and efficient sampling from the simplicial configuration model.

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multinode interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model.

Finite-size analysis of the detectability limit of the stochastic block model.

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large.

Growing networks of overlapping communities with internal structure.

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates.

Constrained growth of complex scale-independent systems.

Scale independence is a ubiquitous feature of complex systems that implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution, and stock actions all feature scale independence. Assuming that they simply do, we focus here on describing how this behavior emerges, in contrast to more idealized models usually considered.

Complex networks as an emerging property of hierarchical preferential attachment.

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment.

General and exact approach to percolation on random graphs.

We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs.

A Shadowing Problem in the Detection of Overlapping Communities: Lifting the Resolution Limit through a Cascading Procedure.

Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks.