Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and heterogeneity of realistic contact dynamics. In this article, we consider Bayesian inference on the spreading parameters of an SIR contagion on a known, static network, where information regarding individual disease status is known only from a series of tests (positive or negative disease status). When the contagion model is complex or information such as infection and removal times is missing, the posterior distribution can be difficult to sample from. Previous work has considered the use of Approximate Bayesian Computation (ABC), which allows for simulation-based Bayesian inference on complex models. However, ABC methods usually require the user to select reasonable summary statistics. Here, we consider an inference scheme based on the Mixture Density Network compressed ABC, which minimizes the expected posterior entropy in order to learn informative summary statistics. This allows us to conduct Bayesian inference on the parameters of a partially observed contagious process while also circumventing the need for manual summary statistic selection. This methodology can be extended to incorporate additional simulation complexities, including behavioural change after positive tests or false test results.

There are two prominent paradigms for the modelling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the second, referred to as the probabilistic approach, one describes a model that specifies the likelihood of observing a given network. Mechanistic models (models developed based on the mechanistic approach) are appealing because they capture scientific processes that are believed to be responsible for network generation; however, they do not easily lend themselves to the use of inferential techniques when compared with probabilistic models. We introduce a general framework for converting a mechanistic network model (MNM) to a probabilistic network model (PNM). The proposed framework makes it possible to identify the essential network properties and their joint probability distribution for some MNMs; doing so makes it possible to address questions such as whether two different mechanistic models generate networks with identical distributions of properties, or whether a network property, such as clustering, is over- or under-represented in the networks generated by the model of interest compared with a reference model. The proposed framework is intended to bridge some of the gap that currently exists between the formulation and representation of mechanistic and PNMs. We also highlight limitations of PNMs that need to be addressed in order to close this gap.

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that includes all possible measures of path length for weighted graphs. The result, without breaking the graph into smaller components, is a distance backbone subgraph sufficient to compute all shortest paths. This is important for understanding the dynamics of spread and communication phenomena in real-world networks. The general methodology we formally derive yields a principled graph reduction technique and provides a finer characterization of the triangular geometry of all edges-those that contribute to shortest paths and those that do not but are involved in other network phenomena. We demonstrate that the distance backbone is very small in large networks across domains ranging from air traffic to the human brain connectome, revealing that network robustness to attacks and failures seems to stem from surprisingly vast amounts of redundancy.

This article proposes a unique approach to bring out the potential of graph-based features to reveal the hidden signatures of wet (WE) and dry (DE) cough signals, which are the suggestive symptoms of various respiratory ailments like COVID 19. The spectral and complex network analyses of 115 cough signals are employed for perceiving the airflow dynamics through the infected respiratory tract while coughing. The different phases of WE and DE are observed from their time-domain signals, indicating the operation of the glottis. The wavelet analysis of WE shows a frequency spread due to the turbulence in the respiratory tract. The complex network features namely degree centrality, eigenvector centrality, transitivity, graph density and graph entropy not only distinguish WE and DE but also reveal the associated airflow dynamics. A better distinguishability between WE and DE is obtained through the supervised machine learning techniques (MLTs)-quadratic support vector machine and neural net pattern recognition (NN), when compared to the unsupervised MLT, principal component analysis. The 93.90% classification accuracy with a precision of 97.00% suggests NN as a better classifier using complex network features. The study opens up the possibility of complex network analysis in remote auscultation.

We use mobile device data to construct empirical interpersonal physical contact networks in the city of Portland, Oregon, both before and after social distancing measures were enacted during the COVID-19 pandemic. These networks reveal how social distancing measures and the public's reaction to the incipient pandemic affected the connectivity patterns within the city. We find that as the pandemic developed there was a substantial decrease in the number of individuals with many contacts. We further study the impact of these different network topologies on the spread of COVID-19 by simulating an SEIR epidemic model over these networks and find that the reduced connectivity greatly suppressed the epidemic. We then investigate how the epidemic responds when part of the population is vaccinated, and we compare two vaccination distribution strategies, both with and without social distancing. Our main result is that the heavy-tailed degree distribution of the contact networks causes a targeted vaccination strategy that prioritizes high-contact individuals to reduce the number of cases far more effectively than a strategy that vaccinates individuals at random. Combining both targeted vaccination and social distancing leads to the greatest reduction in cases, and we also find that the marginal benefit of a targeted strategy as compared to a random strategy exceeds the marginal benefit of social distancing for reducing the number of cases. These results have important implications for ongoing vaccine distribution efforts worldwide.

We analyse officially procured data detailing the COVID-19 transmission in Romania's capital Bucharest between 1st August and 31st October 2020. We apply relational hyperevent models on 19,713 individuals with 13,377 infection ties to determine to what degree the disease spread is affected by age whilst controlling for other covariate and human-to-human transmission network effects. We find that positive cases are more likely to nominate alters of similar age as their sources of infection, thus providing evidence for age homophily. We also show that the relative infection risk is negatively associated with the age of peers, such that the risk of infection increases as the average age of contacts decreases. Additionally, we find that adults between the ages 35 and 44 are pivotal in the transmission of the disease to other age groups. Our results may contribute to better controlling future COVID-19 waves, and they also point to the key age groups which may be essential for vaccination given their prominent role in the transmission of the virus.

Human mobility networks are crucial for a better understanding and controlling the spread of epidemics. Here, we study the impact of human mobility networks on the COVID-19 onset in 203 different countries. We use exponential random graph models to perform an analysis of the country-to-country global spread of COVID-19. We find that most countries had similar levels of virus spreading, with only a few acting as the main global transmitters. Our evidence suggests that migration and tourism inflows increase the probability of COVID-19 case importations while controlling for contiguity, continent co-location and sharing a language. Moreover, we find that air flights were the dominant mode of transportation while male and returning travellers were the main carriers. In conclusion, a mix of mobility and geography factors predicts the COVID-19 global transmission from one country to another. These findings have implications for non-pharmaceutical public health interventions and the management of transborder human circulation.

Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

Network models are applied across many domains where data can be represented as a network. Two prominent paradigms for modelling networks are statistical models (probabilistic models for the observed network) and mechanistic models (models for network growth and/or evolution). Mechanistic models are better suited for incorporating domain knowledge, to study effects of interventions (such as changes to specific mechanisms) and to forward simulate, but they typically have intractable likelihoods. As such, and in a stark contrast to statistical models, there is a relative dearth of research on model selection for such models despite the otherwise large body of extant work. In this article, we propose a simulator-based procedure for mechanistic network model selection that borrows aspects from Approximate Bayesian Computation along with a means to quantify the uncertainty in the selected model. To select the most suitable network model, we consider and assess the performance of several learning algorithms, most notably the so-called Super Learner, which makes our framework less sensitive to the choice of a particular learning algorithm. Our approach takes advantage of the ease to forward simulate from mechanistic network models to circumvent their intractable likelihoods. The overall process is flexible and widely applicable. Our simulation results demonstrate the approach's ability to accurately discriminate between competing mechanistic models. Finally, we showcase our approach with a protein-protein interaction network model from the literature for yeast ().

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e. the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g. independent cascading models) or discontinuous phase transitions (e.g. threshold models). We conclude the review with a summary and an outlook.

An emerging area of research in cognitive science is the utilization of networks to model the structure and processes of the mental lexicon in healthy and clinical populations, like aphasia. Previous research has focused on only one type of word similarity at a time (e.g., semantic relationships), even though words are multi-faceted. Here, we investigate lexical retrieval in a picture naming task from people with Broca's and Wernicke's aphasia and healthy controls by utilizing a multiplex network structure that accounts for the interplay between multiple semantic and phonological relationships among words in the mental lexicon. Extending upon previous work, we focused on the global network measure of closeness centrality which is known to capture spreading activation, an important process supporting lexical retrieval. We conducted a series of logistic regression models predicting the probability of correct picture naming. We tested whether multiplex closeness centrality was a better predictor of picture naming performance than single-layer closeness centralities, other network measures assessing local and meso-scale structure, psycholinguistic variables and group differences. We also examined production gaps, or the difference between the likelihood of producing a word with the lowest and highest closeness centralities. Our results indicated that multiplex closeness centrality was a significant predictor of picture naming performance, where words with high closeness centrality were more likely to be produced than words with low closeness centrality. Additionally, multiplex closeness centrality outperformed single-layer closeness centralities and other multiplex network measures, and remained a significant predictor after controlling for psycholinguistic variables and group differences. Furthermore, we found that the facilitative effect of closeness centrality was similar for both types of aphasia. Our results underline the importance of integrating multiple measures of word similarities in cognitive language networks for better understanding lexical retrieval in aphasia, with an eye towards future clinical applications.

We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.

We describe a class of new algorithms to construct bipartite networks that preserves a prescribed degree and joint-degree (degree-degree) distribution of the nodes. Bipartite networks are graphs that can represent real-world interactions between two disjoint sets, such as actor-movie networks, author-article networks, co-occurrence networks, and heterosexual partnership networks. Often there is a strong correlation between the degree of a node and the degrees of the neighbors of that node that must be preserved when generating a network that reflects the structure of the underling system. Our bipartite 2 (2) algorithms generate an ensemble of networks that preserve prescribed degree sequences for the two disjoint set of nodes in the bipartite network, and the joint-degree distribution that is the distribution of the degrees of all neighbors of nodes with the same degree. We illustrate the effectiveness of the algorithms on a romance network using the NetworkX software environment to compare other properties of a target network that are not directly enforced by the 2 algorithms. We observe that when average degree of nodes is low, as is the case for romance and heterosexual partnership networks, then the 2 networks tend to preserve additional properties, such as the cluster coefficients, than algorithms that do not preserve the joint-degree distribution of the original network.

The London Underground is one of the largest, oldest and most widely used systems of public transit in the world. Transportation in London is constantly challenged to expand and adapt its system to meet the changing requirements of London's populace while maintaining a cost-effective and efficient network. Previous studies have described this system using concepts from graph theory, reporting network diagnostics and core-periphery architecture. These studies provide information about the basic structure and efficiency of this network; however, the question of system optimization in the context of evolving demands is seldom investigated. In this paper we examined the cost effectiveness of the topological-physical embedding of the Tube using estimations of the topological dimension, wiring length and Rentian scaling, an isometric scaling relationship between the number of elements and connections in a system. We measured these properties in both two- and three-dimensional embeddings of the networks into Euclidean space, as well as between two time points, and across the densely interconnected core and sparsely interconnected periphery. While the two- and three-dimensional representations of the present-day Tube exhibit Rentian scaling relationships between nodes and edges of the system, the overall network is approximately cost-efficiently embedded into its physical environment in two dimensions, but not in three. We further investigated a notable disparity in the topology of the network's local core versus its more extended periphery, suggesting an underlying relationship between meso-scale structure and physical embedding. The collective findings from this study, including changes in Rentian scaling over time, provide evidence for differential embedding efficiency in planned versus self-organized networks. These findings suggest that concepts of optimal physical embedding can be applied more broadly to other physical systems whose links are embedded in a well-defined space, and whose topology is constrained by a cost function that minimizes link lengths within that space.

Structure and dynamics of complex systems are often described using weighted networks in which the position, weight and direction of links quantify how activity propagates between system elements, or nodes. Nodes with only few outgoing links of low weight have low out-strength and thus form bottlenecks that hinder propagation. It is currently not well understood how systems can overcome limits imposed by such bottlenecks. Here, we simulate activity cascades on weighted networks and show that, for any cascade length, activity initially propagates towards high out-strength nodes before terminating in low out-strength bottlenecks. Increasing the weights of links that are active early in the cascade further enhances already strong pathways, but worsens the bottlenecks thereby limiting accessibility to other pathways in the network. In contrast, strengthening only links that propagated the activity just prior to cascade termination, i.e. links that point into bottlenecks, eventually removes these bottlenecks and increases the accessibility of all paths on the network. This local adaptation rule simply relies on the relative timing to a global failure signal and allows systems to overcome engrained structure to adapt to new challenges.

We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient estimation of the polynomial permits characterizing and distinguishing very large networks in ways that are are dynamically relevant. Furthermore, a generalization of flows and cuts to structures that determine the reliability suggests a new measure of edge or vertex centrality that we call . We describe how criticality is related to the more common notion of betweenness and illustrate its application to targeting interventions to control outbreaks of infectious disease. Although our applications are to infectious disease outbreaks, the methods we develop are applicable to many other diffusive dynamical systems over complex networks.