Random graph models of social networks

PSA-GNN: An augmented GNN framework with priori subgraph knowledge

Graph neural networks have become the primary graph representation learning paradigm, in which nodes update their embeddings by aggregating messages from their neighbors iteratively. However, current message passing based GNNs exploit the higher-order subgraph information other than 1st-order neighbors insufficiently. In contrast, the long-standing graph research has investigated various subgraphs such as motif, clique, core, and truss that contain important structural information to downstream tasks like node classification, which deserve to be preserved by GNNs. In this work, we propose to use the pre-mined subgraphs as priori knowledge to extend the receptive field of GNNs and enhance their expressive power to go beyond the 1st-order Weisfeiler-Lehman isomorphism test. For that, we introduce a general framework called PSA-GNN (Priori Subgraph Augmented Graph Neural Network), which augments each GNN layer by a pair of parallel convolution layers based on a bipartite graph between nodes and priori subgraphs. PSA-GNN intrinsically builds a hybrid receptive field by incorporating priori subgraphs as neighbors, while the embeddings and weights of subgraphs are trainable. Moreover, PSA-GNN can purify the noisy subgraphs both heuristically before training and deterministically during training based on a novel metric called homogeneity. Experimental results show that PSA-GNN achieves an improved performance compared with state-of-the-art message passing based GNN models.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

A social network analysis of college students' online learning during the epidemic era: A triadic reciprocal determinism perspective

The way in which college students learn online has dramatically altered due to the COVID-19 pandemic. Using the triadic reciprocal determinism (TRD) theory, this study aimed to identify the key factors influencing college students' online learning experience through sentiment analysis, text mining, and social network analysis (SNA). Macro- and micro-level parsing was conducted on the SNA model, which was divided into core, mantle, and shell layers to determine the most influential factors in the core layer. This study found that learners' personal factors, learning behaviors, and related elements in the online learning environment significantly influenced the learning outcomes of college students enrolled in online courses. Additionally, this study explored the distribution of SNA model elements in the mantle and peripheral shell layers, which also impact the online learning experience of college students. Overall, this study provides a comprehensive overview of the various factors affecting college students' online learning experience, and highlights the importance of considering these factors when designing online learning environments for college students.

Nonrandom behavior in the projection of random bipartite networks

There are two main categories of networks studied in the complexity physics community: Monopartite and bipartite networks. In this paper, we present a general framework that provides insights into the connection between these two classes. When a random bipartite network is projected into a monopartite network, under quite general conditions, the result is a nonrandom monopartite network, the features of which can be studied analytically. Unlike previous studies in the physics literature on complex networks, which rely on sparse-network approximations, we provide a complete analysis, focusing on the degree distribution and the clustering coefficient. Our findings primarily offer a technical contribution, adding to the current body of literature by enhancing the understanding of bipartite networks within the community of physicists. In addition, our model emphasizes the substantial difference between the information that can be extracted from a network measuring its degree distribution, or using higher-order metrics such as the clustering coefficient. We believe that our results are general and have broad real-world implications.

Integration or fragmentation: the arrow of China's lithium product development

Lithium is an indispensable resource for the next generation of clean technology. Promoting the development of lithium industry has become a global consensus, with China being no exception. The development process involves not only the growth and degeneration of lithium products but also the path-dependency issues arising from resources and technology. This study, based on the perspective of product space structure, constructs China's lithium product network to study its pattern evolution and predict the development direction. Then, according to the current situation and pattern evolution trends, potential advantageous lithium products and advantage-degraded lithium products are identified, and tactics for expanding chains and breaking chains are formulated for them, presenting strategies for the integrated and fragmentated development of China's lithium products. This aims to steer China's lithium products towards a more orderly and closely interconnected direction, representing the arrow of development for China's lithium products.

Disentangling Jenny's equation by machine learning

The so-called soil-landscape model is the central paradigm which relates soil types to their forming factors through the visionary Jenny's equation. This is a formal mathematical expression that would permit to infer which soil should be found in a specific geographical location if the involved relationship was sufficiently known. Unfortunately, Jenny's is only a conceptual expression, where the intervening variables are of qualitative nature, not being then possible to work it out with standard mathematical tools. In this work, we take a first step to unlock this expression, showing how Machine Learning can be used to predictably relate soil types and environmental factors. Our method outperforms other conventional statistical analyses that can be carried out on the same forming factors defined by measurable environmental variables.

Is the type and/or co-existence of degenerative spinal pathology associated with the occurrence of degenerative cervical myelopathy? A single centre retrospective analysis of individuals with MRI defined cervical cord compression

BACKGROUND

Degenerative cervical myelopathy (DCM) arises from spinal degenerative changes injuring the cervical spinal cord. Most cord compression is incidental, referred to as asymptomatic spinal cord compression (ASCC). How and why ASCC differs from DCM is poorly understood. In this paper, we study a local cohort to identify specific types and groups of degenerative pathology more likely associated with DCM than ASCC.

METHODS

This study was a retrospective cohort analysis (IRB Approval ID: PRN10455). The frequency of degenerative findings between those with ASCC and DCM patients were compared using network analysis, hierarchical clustering, and comparison to existing literature to identify potential subgroups in a local cohort (N = 155) with MRI-defined cervical spinal cord compression. Quantitative measures of spinal cord compression (MSCC and MCC) were used to confirm their relevance.

RESULTS

ELF (8.7 %, 95 % CI 3.8-13.6 % vs 35.7 %, 95 % CI 27.4-44.0 %) Congenital Stenosis (3.9 %, 95 % CI 0.6-7.3 % vs 25.0 %, 95 % CI 17.5-32.5 %), and OPLL (0.0 %, 95 % CI 0.0-0.0 % vs 3.6 %, 95 % CI 0.3-6.8 %) were more likely in patients with DCM. Comparative network analysis indicated loss of lordosis was associated with ASCC, whilst ELF with DCM. Hierarchical Cluster Analysis indicated four sub-groups: multi-level disc disease with ELF, single-level disc disease without loss of lordosis and OPLL with DCM, and single-level disc disease with loss of lordosis with ASCC. Quantitative measures of cord compression were higher in groups associated with DCM, but similar in patients with single-level disc disease and loss of lordosis.

CONCLUSIONS

This study identified four subgroups based on degenerative pathology requiring further investigation.

Analysis of functional connectivity using machine learning and deep learning in different data modalities from individuals with schizophrenia

Objective. Schizophrenia(SCZ) is a severe mental disorder associated with persistent or recurrent psychosis, hallucinations, delusions, and thought disorders that affect approximately 26 million people worldwide, according to the World Health Organization. Several studies encompass machine learning (ML) and deep learning algorithms to automate the diagnosis of this mental disorder. Others study SCZ brain networks to get new insights into the dynamics of information processing in individuals suffering from the condition. In this paper, we offer a rigorous approach with ML and deep learning techniques for evaluating connectivity matrices and measures of complex networks to establish an automated diagnosis and comprehend the topology and dynamics of brain networks in SCZ individuals.Approach.For this purpose, we employed an functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) dataset. In addition, we combined EEG measures, i.e. Hjorth mobility and complexity, with complex network measurements to be analyzed in our model for the first time in the literature.Main results.When comparing the SCZ group to the control group, we found a high positive correlation between the left superior parietal lobe and the left motor cortex and a positive correlation between the left dorsal posterior cingulate cortex and the left primary motor. Regarding complex network measures, the diameter, which corresponds to the longest shortest path length in a network, may be regarded as a biomarker because it is the most crucial measure in different data modalities. Furthermore, the SCZ brain networks exhibit less segregation and a lower distribution of information. As a result, EEG measures outperformed complex networks in capturing the brain alterations associated with SCZ.Significance. Our model achieved an area under receiver operating characteristic curve (AUC) of 100% and an accuracy of 98.5% for the fMRI, an AUC of 95%, and an accuracy of 95.4% for the EEG data set. These are excellent classification results. Furthermore, we investigated the impact of specific brain connections and network measures on these results, which helped us better describe changes in the diseased brain.

Universality of explosive percolation under product and sum rule

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M-1 candidate edges are being discarded. These two rules are prototypical "explosive" percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.

Generic properties of the oligodendrocyte - axon network

The role of oligodendrocytes (OLs) extends beyond saltatory conduction to a modulatory role in neural information processing. Given this exalted role, we take first steps to frame the OL - axon interaction as a network of cells. We find that the OL - axon network has a natural encoding as a bipartite network, allowing us to determine key network properties, estimate the number of OLs or axons in various brain regions and determine the robustness of the network to random removal of cell nodes.

Diagnosis of autism spectrum disorder based on functional brain networks and machine learning

Autism is a multifaceted neurodevelopmental condition whose accurate diagnosis may be challenging because the associated symptoms and severity vary considerably. The wrong diagnosis can affect families and the educational system, raising the risk of depression, eating disorders, and self-harm. Recently, many works have proposed new methods for the diagnosis of autism based on machine learning and brain data. However, these works focus on only one pairwise statistical metric, ignoring the brain network organization. In this paper, we propose a method for the automatic diagnosis of autism based on functional brain imaging data recorded from 500 subjects, where 242 present autism spectrum disorder considering the regions of interest throughout Bootstrap Analysis of Stable Cluster map. Our method can distinguish the control group from autism spectrum disorder patients with high accuracy. Indeed the best performance provides an AUC near 1.0, which is higher than that found in the literature. We verify that the left ventral posterior cingulate cortex region is less connected to an area in the cerebellum of patients with this neurodevelopment disorder, which agrees with previous studies. The functional brain networks of autism spectrum disorder patients show more segregation, less distribution of information across the network, and less connectivity compared to the control cases. Our workflow provides medical interpretability and can be used on other fMRI and EEG data, including small data sets.

Recent trends in interorganizational deal networks in pharmaceutical and biotechnology industries

While there have been trends in drug discovery from small molecules to new chemical modalities since the large mergers and acquisitions (M&A) of pharmaceutical companies in the late 2000s, trends in interorganizational deal networks have not been well addressed. We investigated the changing trends in interorganizational deals in the pharmaceutical and biotechnology industries. The results demonstrated that there have been changing trends, including a growing number of spinouts from academia and M&A in the United States and Europe. These findings indicates that the traditional network in which large pharmaceutical companies drove drug discovery output has changed, and interorganizational deals among diverse players have become more active.

Scaling of ant colony interaction networks

In social insect colonies, individuals are physically independent but functionally integrated by interaction networks which provide a foundation for communication and drive the emergence of collective behaviors, including nest architecture, division of labor, and potentially also the social regulation of metabolic rates. To investigate the relationship between interactions, metabolism, and colony size, we varied group size for harvester ant colonies (Pogonomyrmex californicus) and assessed their communication networks based on direct antennal contacts and compared these results with proximity networks and a random movement simulation. We found support for the hypothesis of social regulation; individuals did not interact with each other randomly but exhibited restraint. Connectivity scaled hypometrically with colony size, per-capita interaction rate was scale-invariant, and smaller colonies exhibited higher measures of closeness centrality and edge density, correlating with higher per-capita metabolic rates. Although the immediate energetic cost for two ants to interact is insignificant, the downstream effects of receiving and integrating social information can have metabolic consequences. Our results indicate that individuals in larger colonies are relatively more insulated from each other, a factor that may reduce or filter noisy stimuli and contribute to the hypometric scaling of their metabolic rates, and perhaps more generally, the evolution of larger colony sizes.

Application of machine learning and complex network measures to an EEG dataset from ayahuasca experiments

Ayahuasca is a blend of Amazonian plants that has been used for traditional medicine by the inhabitants of this region for hundreds of years. Furthermore, this plant has been demonstrated to be a viable therapy for a variety of neurological and mental diseases. EEG experiments have found specific brain regions that changed significantly due to ayahuasca. Here, we used an EEG dataset to investigate the ability to automatically detect changes in brain activity using machine learning and complex networks. Machine learning was applied at three different levels of data abstraction: (A) the raw EEG time series, (B) the correlation of the EEG time series, and (C) the complex network measures calculated from (B). Further, at the abstraction level of (C), we developed new measures of complex networks relating to community detection. As a result, the machine learning method was able to automatically detect changes in brain activity, with case (B) showing the highest accuracy (92%), followed by (A) (88%) and (C) (83%), indicating that connectivity changes between brain regions are more important for the detection of ayahuasca. The most activated areas were the frontal and temporal lobe, which is consistent with the literature. F3 and PO4 were the most important brain connections, a significant new discovery for psychedelic literature. This connection may point to a cognitive process akin to face recognition in individuals during ayahuasca-mediated visual hallucinations. Furthermore, closeness centrality and assortativity were the most important complex network measures. These two measures are also associated with diseases such as Alzheimer's disease, indicating a possible therapeutic mechanism. Moreover, the new measures were crucial to the predictive model and suggested larger brain communities associated with the use of ayahuasca. This suggests that the dissemination of information in functional brain networks is slower when this drug is present. Overall, our methodology was able to automatically detect changes in brain activity during ayahuasca consumption and interpret how these psychedelics alter brain networks, as well as provide insights into their mechanisms of action.

Quantum physics in connected worlds

Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small fraction of the pairs of the constituents directly interact. Motivated by advances in control over the pairwise interactions in many-body simulators, we determine the fate of spin systems on more general, arbitrary graphs. Placing the minimum possible constraints on the underlying graph, we prove how, with certainty in the thermodynamic limit, such systems behave like a single collective spin. We thus understand the emergence of complex many-body physics as dependent on 'exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of dense graphs we identify hitherto unknown exceptions via their inhomogeneity and observe how complexity is heralded in these systems by entanglement and highly non-uniform correlation functions. Our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter.

Dependency Structures in Cryptocurrency Market from High to Low Frequency

We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve from high (15 s) to low (1 day) frequency time resolutions. For each horizon, we test the stability, statistical significance and economic meaningfulness of the networks. Results give a deep insight into the evolutionary process of the time dependent hierarchical organization of the system under analysis. A decrease in correlation between pairs of cryptocurrencies is observed for finer time sampling resolutions. A growing structure emerges for coarser ones, highlighting multiple changes in the hierarchical reference role played by mainstream cryptocurrencies. This effect is studied both in its pairwise realizations and intra-sector ones.

Modelling Spirals of Silence and Echo Chambers by Learning from the Feedback of Others

What are the mechanisms by which groups with certain opinions gain public voice and force others holding a different view into silence? Furthermore, how does social media play into this? Drawing on neuroscientific insights into the processing of social feedback, we develop a theoretical model that allows us to address these questions. In repeated interactions, individuals learn whether their opinion meets public approval and refrain from expressing their standpoint if it is socially sanctioned. In a social network sorted around opinions, an agent forms a distorted impression of public opinion enforced by the communicative activity of the different camps. Even strong majorities can be forced into silence if a minority acts as a cohesive whole. On the other hand, the strong social organisation around opinions enabled by digital platforms favours collective regimes in which opposing voices are expressed and compete for primacy in public. This paper highlights the role that the basic mechanisms of social information processing play in massive computer-mediated interactions on opinions.

Learning to predict synchronization of coupled oscillators on randomly generated graphs

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators-the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an "ensemble prediction" algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.

An empirical Bayes approach to stochastic blockmodels and graphons: shrinkage estimation and model selection

The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. Estimation of the graphon function has gained a lot of recent research interests. Most existing works focus on inference in the latent space of the model, while adopting simple maximum likelihood or Bayesian estimates for the graphon or connectivity parameters given the identified latent variables. In this work, we propose a hierarchical model and develop a novel empirical Bayes estimate of the connectivity matrix of a stochastic block model to approximate the graphon function. Based on our hierarchical model, we further introduce a new model selection criterion for choosing the number of communities. Numerical results on extensive simulations and two well-annotated social networks demonstrate the superiority of our approach in terms of parameter estimation and model selection.

Opinion polarization in social networks

In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Adversarial Attack on Skeleton-Based Human Action Recognition

Deep learning models achieve impressive performance for skeleton-based human action recognition. Graph convolutional networks (GCNs) are particularly suitable for this task due to the graph-structured nature of skeleton data. However, the robustness of these models to adversarial attacks remains largely unexplored due to their complex spatiotemporal nature that must represent sparse and discrete skeleton joints. This work presents the first adversarial attack on skeleton-based action recognition with GCNs. The proposed targeted attack, termed constrained iterative attack for skeleton actions (CIASA), perturbs joint locations in an action sequence such that the resulting adversarial sequence preserves the temporal coherence, spatial integrity, and the anthropomorphic plausibility of the skeletons. CIASA achieves this feat by satisfying multiple physical constraints and employing spatial skeleton realignments for the perturbed skeletons along with regularization of the adversarial skeletons with generative networks. We also explore the possibility of semantically imperceptible localized attacks with CIASA and succeed in fooling the state-of-the-art skeleton action recognition models with high confidence. CIASA perturbations show high transferability in black-box settings. We also show that the perturbed skeleton sequences are able to induce adversarial behavior in the RGB videos created with computer graphics. A comprehensive evaluation with NTU and Kinetics data sets ascertains the effectiveness of CIASA for graph-based skeleton action recognition and reveals the imminent threat to the spatiotemporal deep learning tasks in general.

Diversity in valuing social contact and risk tolerance leading to the emergence of homophily in populations facing infectious threats

How self-organization leads to the emergence of structure in social populations remains a fascinating and open question in the study of complex systems. One frequently observed structure that emerges again and again across systems is that of self-similar community, i.e., homophily. We use a game theoretic perspective to explore a case in which individuals choose affiliation partnerships based on only two factors: the value they place on having social contacts, and their risk tolerance for exposure to threat derived from social contact (e.g., infectious disease, threatening ideas, etc.). We show how diversity along just these two influences is sufficient to cause the emergence of self-organizing homophily in the population. We further consider a case in which extrinsic social factors influence the desire to maintain particular social ties, and show the robustness of emergent homophilic patterns to these additional influences. These results demonstrate how observable population-level homophily may arise out of individual behaviors that balance the value of social contacts against the potential risks associated with those contacts. We present and discuss these results in the context of outbreaks of infectious disease in human populations. Complementing the standard narrative about how social division alters epidemiological risk, we here show how epidemiological risk may deepen social divisions in human populations.

Individual versus social benefit on heterogeneous networks

The focus of structural balance theory is dedicated to social benefits, while in a real network individual benefits sometimes are the focus as well. The Strauss's model addresses individual benefits besides the social one with a simple assumption that all individual benefits are equivalent. Therefore, the results show that the competition between two terms leads to a phase transition between individual and social benefits and there is a critical point CP that represents a first-order phase transition in the network. Concerning a real network of relations, individuals adjust the strength of their relationships based on the benefits they acquire from them. Hence, by addressing heterogeneity in the individual interactions, we study a modified version of Strauss's model in which the first term represents the heterogeneous individual benefits by θ_{ij}, and the coefficient of the second term, α, measures the strength of social benefits. Our studies show that there is a region where the triangles are in a crumpled state rather than being dispersed in the network; furthermore, increasing the heterogeneity of individual benefits results in the narrower region of the crumpled state. Outside of the mentioned region, the network is a mixture of links and triangles and the value of α determines whether the individual benefit or social benefit dominates. For the small value of α, the individual benefit dominates, whereas in the large value of α, the social benefit dominates.

A network SIRX model for the spreading of COVID-19

Infectious diseases, such as the current COVID-19, have a huge economic and societal impact. The ability to model its transmission characteristics is critical to minimize its impact. In fact, predicting how fast an infection is spreading could be a major factor in deciding on the severity, extent and strictness of the applied mitigation measures, such as the recent lockdowns. Even though modelling epidemics is a well studied subject, usually models do not include quarantine or other social measures, such as those imposed in the recent pandemic. The current work builds upon a recent paper by Maier and Brockmann (2020), where a compartmental SIRX model was implemented. That model included social or individual behavioural changes during quarantine, by introducing state X , in which symptomatic quarantined individuals are not transmitting the infection anymore, and described well the transmission in the initial stages of the infection. The results of the model were applied to real data from several provinces in China, quite successfully. In our approach we use a Monte-Carlo simulation model on networks. Individuals are network nodes and the links are their contacts. We use a spreading mechanism from the initially infected nodes to their nearest neighbours, as has been done previously. Initially, we find the values of the rate constants (parameters) the same way as in Maier and Brockmann (2020) for the confirmed cases of a country, on a daily basis, as given by the Johns Hopkins University. We then use different types of networks (random Erdős-Rényi, Small World, and Barabási-Albert Scale-Free) with various characteristics in an effort to find the best fit with the real data for the same geographical regions as reported in Maier and Brockmann (2020). Our simulations show that the best fit comes with the Erdős-Rényi random networks. We then apply this method to several other countries, both for large-size countries, and small size ones. In all cases investigated we find the same result, i.e. best agreement for the evolution of the pandemic with time is for the Erdős-Rényi networks. Furthermore, our results indicate that the best fit occurs for a random network with an average degree of the order of〈 k 〉 ≈ 10-25, for all countries tested. Scale Free and Small World networks fail to fit the real data convincingly.

Statistical physics of exchangeable sparse simple networks, multiplex networks, and simplicial complexes

Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabeling of the nodes. However, combining sparsity of network ensembles with exchangeability is challenging. Here we propose a statistical physics framework and a Metropolis-Hastings algorithm defining exchangeable sparse network ensembles. The model generates networks with heterogeneous degree distributions by enforcing only global constraints while existing (nonexchangeable) exponential random graphs enforce an extensive number of local constraints. This very general theoretical framework to describe exchangeable networks is here first formulated for uncorrelated simple networks and then it is extended to treat simple networks with degree correlations, directed networks, bipartite networks, and generalized network structures including multiplex networks and simplicial complexes. In particular here we formulate and treat both uncorrelated and correlated exchangeable ensembles of simplicial complexes using statistical mechanics approaches.

Making graphs compact by lossless contraction

This paper proposes a scheme to reduce big graphs to small graphs. It contracts obsolete parts and regular structures into supernodes. The supernodes carry a synopsis S Q for each query class Q in use, to abstract key features of the contracted parts for answering queries of Q . Moreover, for various types of graphs, we identify regular structures to contract. The contraction scheme provides a compact graph representation and prioritizes up-to-date data. Better still, it is generic and lossless. We show that the same contracted graph is able to support multiple query classes at the same time, no matter whether their queries are label based or not, local or non-local. Moreover, existing algorithms for these queries can be readily adapted to compute exact answers by using the synopses when possible and decontracting the supernodes only when necessary. As a proof of concept, we show how to adapt existing algorithms for subgraph isomorphism, triangle counting, shortest distance, connected component and clique decision to contracted graphs. We also provide a bounded incremental contraction algorithm in response to updates, such that its cost is determined by the size of areas affected by the updates alone, not by the entire graphs. We experimentally verify that on average, the contraction scheme reduces graphs by 71.9% and improves the evaluation of these queries by 1.69, 1.44, 1.47, 2.24 and 1.37 times, respectively.

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

Comprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccine supplies are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-CoV-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies, using a generalized multi-site mean-field model, which can naturally assess the impact of manual and digital approaches alike. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of more complex pathogen dynamics. We use this technique to simulate a newly-defined epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

Analysis of Korean Peninsula Earthquake Network Based on Event Shuffling and Network Shuffling

In this work, a Korean peninsula earthquake network, constructed via event-sequential linking known as the Abe–Suzuki method, was investigated in terms of network properties. A significance test for these network properties was performed via comparisons with those of two random networks, constructed from two approaches, that is, EVENT (SEQUENCE) SHUFFLING and NETWORK (MATRIX) SHUFFLING. The Abe–Suzuki earthquake network has a clear difference from the two random networks. However, the two shuffled networks exhibited completely different functions, and even some network properties for one shuffled datum are significantly high and those of the other shuffled data are low compared to actual data. For most cases, the event-shuffled network showed a functional similarity to the real network, but with different exponents/parameters. This result strongly claims that the Korean peninsula earthquake network has a spatiotemporal causal relation. Additionally, the Korean peninsula network properties are mostly similar to those found in previous studies on the US and Japan. Further, the Korean earthquake network showed strong linearity in a specific range of spatial resolution, that is, 0.20°~0.80°, implying that macroscopic properties of the Korean earthquake network are highly regular in this range of resolution.

Dynamics of majority rule on hypergraphs

A broad range of dynamical systems involve multibody interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, namely the majority rule, and we investigate the possibility to represent and analyze the system by means of hypergraphs. We explore the formation of consensus, and we restrict our attention to interaction groups of size 3 in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or mean-field heterogeneity, and we recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

What is the Purpose of this Meeting? The hidden meanings of the meeting announcement

This study examines the coincidence or discrepancy between the purpose of meetings stated in the organizer’s announcement and the purposes perceived by the participants. This analysis enriches and complexifies the view of meeting purposes in the literature. Based on structured questionnaire data from 1,946 respondents involved in 490 meetings conducted in the context of an international project, our analysis shows that the stated and perceived purposes of a meeting are not necessarily the same. In particular, a purpose expressed as a noun (e.g. Coordination) may be perceived by participants as various purposes expressed in verbs, that are strongly or weakly aligned with that noun (e.g. Socialize, Coordinate, Follow up or Persuade). This study establishes the need for a distinct line of research into the discrepancy between stated and perceived meeting purposes to understand meeting-related organizational dynamics, and it lays a basis for theorizing within that line of investigation by demonstrating an influence of the internal-external nature of meetings and the local culture. This study also highlights the core intermediation role of socialization for achieving the stated purposes of certain meeting types. Additionally, this study has immediate implications for organizing and managing meetings.

Application of graph theory in the library domain—Building a faceted framework based on a literature review

Based on a literature review, we present a framework for structuring the application of graph theory in the library domain. Our goal is to provide both researchers and libraries with a standard tool to classify scientific work, at the same time allowing for the identification of previously underrepresented areas where future research might be productive. To achieve this, we compile graph theoretical approaches from the literature to consolidate the components of our framework on a solid basis. The extendable framework consists of multiple facets grouped into five categories whose elements can be arbitrarily combined. Libraries can benefit from these facets by using them as a point of reference for the (meta)data they offer. Further work on formally defining the framework’s categories as well as on integration of other graph-related research areas not discussed in this article (e.g. knowledge graphs) would be desirable and helpful in the future.

The nature of ICT in technology convergence: A knowledge-based network analysis

This study aims to understand the nature of information and communication technology in technology convergence. We form a knowledge network by applying social network theories to Korean patent data collected from the European Patent Organization. A knowledge network consists of nodes representing technology sectors identified by their International Patent Classification codes and edges that link International Patent Classification codes when they appear concurrently in a patent. We test the proposed hypotheses using four indices (degree centrality, E-I index, entropy index, and clustering coefficient). The results show that information and communication technology is easily attached but tends to converge with similar technology and has the greatest influence on technology convergence over other technologies. This study is expected to help practitioners and policymakers understand the structure and interaction mechanisms of technology from a systematic perspective and improve national-level technology policies.

Assessing the fluvial system resilience of the river Bacchiglione to point sources of pollution in Northeast Italy: a novel Water Resilience Index (WRI) approach

Modelling and evaluating the resilience of environmental systems has recently raised significant interest among both practitioners and researchers. However, it has not yet been used to measure the absorption and recovery capacities of a river subject to varying levels of pollution due to natural and anthropic sources of contamination within the basin. Fast worldwide population growth and climate change are contributing to an increased degradation status in surface water bodies and to a decreased efficiency of their natural self-purification processes. Decision-makers are, therefore, more and more encouraged to implement alternative management strategies focussed on improving the system resilience to current and future perturbations. To this end, a novel Water Resilience Index (WRI), based on different quality parameters, was developed, and it is here proposed to estimate the ability of the river Bacchiglione, located in Northeast Italy, absorb continuous and unpredictable changes due to potential effects of point sources of pollution, that is, urban and industrial wastewater, and still maintain its vital functions. This new index is integrated in a mathematical model, which represents the river as an influence diagram where the nodes are the gauged stations and the arcs are the fluvial reaches among the stations, to identify the river reaches in need of resilience improvement. In addition, in order to simplify the analytical procedure and lower the costs and times of the monitoring activities, a principal component analysis is also used, as it is able to reduce the number of the water quality parameters to be collected from the sampling stations, distributed along the main river, and thus to calculate a minimum WRI. The good agreement between the results obtained by both the original and minimum WRI shows the effectiveness of the proposed methodology. This approach could be applied to all basins with the same issues, and not just in the Italian case study here analysed, as it might be a valid tool to plan interventions and mitigation actions, protecting the resource from pollution risks and achieving environmental quality and Sustainable Development Goals both in the water bodies and their surrounding territories. In addition, this strategy could be integrated in the existing models supporting local decision-makers and administrators, aiming at increasing the resilience of urban and rural areas to pollution phenomena and facilitating the development of effective policies to reduce the impacts of global change on water quality.

Livestock Network Analysis for Rhodesiense Human African Trypanosomiasis Control in Uganda

Background: Infected cattle sourced from districts with established foci for Trypanosoma brucei rhodesiense human African trypanosomiasis (rHAT) migrating to previously unaffected districts, have resulted in a significant expansion of the disease in Uganda. This study explores livestock movement data to describe cattle trade network topology and assess the effects of disease control interventions on the transmission of rHAT infectiousness. Methods: Network analysis was used to generate a cattle trade network with livestock data which was collected from cattle traders (n = 197) and validated using random graph methods. Additionally, the cattle trade network was combined with a susceptible, infected, recovered (SIR) compartmental model to simulate spread of rHAT (R o 1.287), hence regarded as "slow" pathogen, and evaluate the effects of disease interventions. Results: The cattle trade network exhibited a low clustering coefficient (0.5) with most cattle markets being weakly connected and a few being highly connected. Also, analysis of the cattle movement data revealed a core group comprising of cattle markets from both eastern (rHAT endemic) and northwest regions (rHAT unaffected area). Presence of a core group may result in rHAT spread to unaffected districts and occurrence of super spreader cattle market or markets in case of an outbreak. The key cattle markets that may be targeted for routine rHAT surveillance and control included Namutumba, Soroti, and Molo, all of which were in southeast Uganda. Using effective trypanosomiasis such as integrated cattle injection with trypanocides and spraying can sufficiently slow the spread of rHAT in the network. Conclusion: Cattle trade network analysis indicated a pathway along which T. b. rhodesiense could spread northward from eastern Uganda. Targeted T. b. rhodesiense surveillance and control in eastern Uganda, through enhanced public-private partnerships, would serve to limit its spread.

Risk spillover networks in financial system based on information theory

Since the financial system has illustrated an increasingly prominent characteristic of inextricable connections, information theory is gradually utilized to study the financial system. By collecting the daily data of industry index (2005-2020) and region index (2012-2020) listed in China as samples, this paper applies an innovative measure named partial mutual information on mixed embedding to generate directed networks. Based on the analysis of nonlinear relationships among sectors, this paper realizes the accurate construction of "time-varying" financial network from the perspective of risk spillover. The results are presented as follow: (1) interactions can be better understood through the nonlinear networks among distinct sectors, and sectors in the networks could be classified into different types according to their topological properties connected to risk spillover; (2) in the rising stage, information is transmitted rapidly in the network, so the risk is fast diffused and absorbed; (3) in the declining stage, the network topology is more complex and panic sentiments have long term impact leading to more connections; (4) The US market, Japan market and Hongkong market have significant affect on China's market. The results suggest that this nonlinear measure is an effective approach to develop financial networks and explore the mechanism of risk spillover.

A social network approach for the study of leprosy transmission beyond the household

BACKGROUND

Mycobacterium leprae was the first microorganism directly associated with a disease, however, there are still important gaps in our understanding of transmission. Although household contacts are prioritized, there is evidence of the importance of extrahousehold contacts. The goal of this article is to contribute to our understanding of the transmission of leprosy ex-household.

METHODS

We compare co-location data of 397 leprosy cases and 211 controls drawn from the Centro de Dermatologia Sanitária D. Libânia in Fortaleza, Brazil. We collected lifetime geolocation data related to residence, school attendance and workplace and developed novel methods to establish a critical distance (Rc) for exposure and evaluated the potential for transmission for residence, school and workplace.

RESULTS

Our methods provide different threshold values of distance for residence, school and workplace. Residence networks demonstrate an Rc of about 500 m. Cases cluster in workplaces as well. Schools do not cluster cases.

CONCLUSIONS

Our novel network approach offers a promising opportunity to explore leprosy transmission. Our networks confirm the importance of coresidence, provide a boundary and suggest a role for transmission in workplaces. Schools, on the other hand, do not demonstrate a clustering of cases. Our findings may have programmatic relevance.

Scale-free percolation in continuous space: quenched degree and clustering coefficient

Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuous-space version of scale-free percolation introduced in [14]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\mathbb{R}^d$. Each vertex is equipped with a random weight, and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree distributions of all the nodes of the graph follow a power law with the same tail at infinity. We also show that the averaged clustering coefficient of the graph is self-averaging. In particular, it is almost surely equal to the annealed clustering coefficient of one point, which is a strictly positive quantity.

Social Network Mediation Analysis: A Latent Space Approach

A social network comprises both actors and the social connections among them. Such connections reflect the dependence among social actors, which is essential for individuals' mental health and social development. In this article, we propose a mediation model with a social network as a mediator to investigate the potential mediation role of a social network. In the model, the dependence among actors is accounted for by a few mutually orthogonal latent dimensions which form a social space. The individuals' positions in such a latent social space are directly involved in the mediation process between an independent and dependent variable. After showing that all the latent dimensions are equivalent in terms of their relationship to the social network and the meaning of each dimension is arbitrary, we propose to measure the whole mediation effect of a network. Although individuals' positions in the latent space are not unique, we rigorously articulate that the proposed network mediation effect is still well defined. We use a Bayesian estimation method to estimate the model and evaluate its performance through an extensive simulation study under representative conditions. The usefulness of the network mediation model is demonstrated through an application to a college friendship network.

The small world of German CEOs: a multi-method analysis of the affiliation network structure

This paper seeks to understand the structure of corporate networks in the period following the dissolution of Deutschland AG (“Germany Inc.”). For this purpose, affiliation networks among chief executive officers (CEOs) that are based on common membership in various societal organizations will be examined. I apply an innovative mix of methods for studying a sample of CEOs from the 100 top companies in Germany in the 2010s. Based on social network analysis, I show that the overall affiliation network has all features of a small-world network, i.e., a high clustering coefficient and a short path length among the CEOs. The average degree of separation among German CEOs is only two steps. Another innovative contribution of this paper is its study of the linkage between affiliation network features and patterns of corporate recruitment. Using multiple correspondence analysis, I show that different subgroups of the overall affiliation network have their specific network characteristics and recruitment patterns. Within the network, managers from automotive and technical engineering often assume brokerage positions, while managers from the trade branch are largely isolated. This study shows that the affiliation networks and corporate recruitment patterns are interlinked; the transformation of corporate networks is a dynamic outcome of interrelations among different subgroups within the network, each with distinct educational, professional, and network characteristics.

Low rattling: A predictive principle for self-organization in active collectives

Self-organization is frequently observed in active collectives as varied as ant rafts and molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally, with the use of shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing toward future approaches for the design and control of active particle mixtures and metamaterials.

Dimension reduction for covariates in network data

A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach, called network-supervised dimension reduction, in which covariates are projected onto low-dimensional spaces to reveal the linkage pattern without assuming a model. We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer proximity in the low-dimension projection corresponds to stronger connections. Interestingly, the convergence rate of our estimator is found to depend on a network effect factor, which is the smallest number that can partition a graph in a manner similar to the graph colouring problem. Our method has interesting connections to principal component analysis and linear discriminant analysis, which we exploit for clustering and community detection. The proposed approach is further illustrated by numerical experiments and analysis of a pulsar candidates dataset from astronomy.

Patent citation network analysis: A perspective from descriptive statistics and ERGMs

Patent Citation Analysis has been gaining considerable traction over the past few decades. In this paper, we collect extensive information on patents and citations and provide a perspective of citation network analysis of patents from a statistical viewpoint. We identify and analyze the most cited patents, the most innovative and the highly cited companies along with the structural properties of the network by providing in-depth descriptive analysis. Furthermore, we employ Exponential Random Graph Models (ERGMs) to analyze the citation networks. ERGMs enables understanding the social perspectives of a patent citation network which has not been studied earlier. We demonstrate that social properties such as homophily (the inclination to cite patents from the same country or in the same language) and transitivity (the inclination to cite references' references) together with the technicalities of the patents (e.g., language, categories), has a significant effect on citations. We also provide an in-depth analysis of citations for sectors in patents and how it is affected by the size of the same. Overall, our paper delves into European patents with the aim of providing new insights and serves as an account for fitting ERGMs on large networks and analyzing them. ERGMs help us model network mechanisms directly, instead of acting as a proxy for unspecified dependence and relationships among the observations.