Reciprocity of weighted networks

Eigenvalue spectra of finely structured random matrices

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are applicable in a myriad of different contexts. However, it is often assumed that all components of the complex system in question are statistically equivalent, which is unrealistic in many applications. Here we introduce the concept of a finely structured random matrix. These are random matrices with element-specific statistics, which can be used to model systems in which the individual components are statistically distinct. By supposing that the degree of "fine structure" in the matrix is small, we arrive at a succinct "modified" elliptical law. We demonstrate the direct applicability of our results to the niche and cascade models in theoretical ecology, as well as a model of a neural network, and a directed network with arbitrary degree distribution. The simple closed form of our central results allow us to draw broad qualitative conclusions about the effect of fine structure on stability.

Commodity-specific triads in the Dutch inter-industry production network

Triadic motifs are the smallest building blocks of higher-order interactions in complex networks and can be detected as over-occurrences with respect to null models with only pair-wise interactions. Recently, the motif structure of production networks has attracted attention in light of its possible role in the propagation of economic shocks. However, its characterization at the level of individual commodities is still poorly understood. Here we analyze both binary and weighted triadic motifs in the Dutch inter-industry production network disaggregated at the level of 187 commodity groups, which Statistics Netherlands reconstructed from National Accounts registers, surveys and known empirical data. We introduce appropriate null models that filter out node heterogeneity and the strong effects of link reciprocity and find that, while the aggregate network that overlays all products is characterized by a multitude of triadic motifs, most single-product layers feature no significant motif, and roughly 85% of the layers feature only two motifs or less. This result paves the way for identifying a simple 'triadic fingerprint' of each commodity and for reconstructing most product-specific networks from partial information in a pairwise fashion by controlling for their reciprocity structure. We discuss how these results can help statistical bureaus identify fine-grained information in structural analyses of interest for policymakers.

Stingy bots can improve human welfare in experimental sharing networks

Machines powered by artificial intelligence increasingly permeate social networks with control over resources. However, machine allocation behavior might offer little benefit to human welfare over networks when it ignores the specific network mechanism of social exchange. Here, we perform an online experiment involving simple networks of humans (496 participants in 120 networks) playing a resource-sharing game to which we sometimes add artificial agents (bots). The experiment examines two opposite policies of machine allocation behavior: reciprocal bots, which share all resources reciprocally; and stingy bots, which share no resources at all. We also manipulate the bot's network position. We show that reciprocal bots make little changes in unequal resource distribution among people. On the other hand, stingy bots balance structural power and improve collective welfare in human groups when placed in a specific network position, although they bestow no wealth on people. Our findings highlight the need to incorporate the human nature of reciprocity and relational interdependence in designing machine behavior in sharing networks. Conscientious machines do not always work for human welfare, depending on the network structure where they interact.

Evolvement patterns of usage in a medium-sized bike-sharing system during the COVID-19 pandemic

The global outbreak of COVID-19 has fundamentally reshaped human mobility. Compared to other modes of transportation, how spatiotemporal patterns of urban bike-sharing have evolved since the outbreak is yet to be fully understood, especially for bike-sharing systems operating on a smaller scale. Taking Pittsburgh as a case study, we examined the changes in spatiotemporal dynamics of shared bike usage from 2019 to 2021. By distinguishing between weekday and weekend usage, we found different temporal patterns between trip volume and duration, and distinct spatial patterns of within- and between-region rides with respect to naturally separated regions. Overall, the results illustrate the resilience and the vital role of bike-sharing during the pandemic, consistent with previous observations on bike-sharing systems of a larger scale. Our study contributes to a comprehensive understanding of bike-sharing that calls for more research on smaller-scale systems under disruptive events such as the pandemic, which can greatly inform decision-makers from smaller sized cities and enable future studies to compare across different urban regions or modes of transportation.

Dynamic structure of motor cortical neuron coactivity carries behaviorally relevant information

Skillful, voluntary movements are underpinned by computations performed by networks of interconnected neurons in the primary motor cortex (M1). Computations are reflected by patterns of coactivity between neurons. Using pairwise spike time statistics, coactivity can be summarized as a functional network (FN). Here, we show that the structure of FNs constructed from an instructed-delay reach task in nonhuman primates is behaviorally specific: Low-dimensional embedding and graph alignment scores show that FNs constructed from closer target reach directions are also closer in network space. Using short intervals across a trial, we constructed temporal FNs and found that temporal FNs traverse a low-dimensional subspace in a reach-specific trajectory. Alignment scores show that FNs become separable and correspondingly decodable shortly after the Instruction cue. Finally, we observe that reciprocal connections in FNs transiently decrease following the Instruction cue, consistent with the hypothesis that information external to the recorded population temporarily alters the structure of the network at this moment.

Evidence of inter-state coordination amongst state-backed information operations

Since 2018, Twitter has steadily released into the public domain content discovered on the platform and believed to be associated with information operations originating from more than a dozen state-backed organizations. Leveraging this dataset, we explore inter-state coordination amongst state-backed information operations and find evidence of intentional, strategic interaction amongst thirteen different states, separate and distinct from within-state operations. We find that coordinated, inter-state information operations attract greater engagement than baseline information operations and appear to come online in service to specific aims. We explore these ideas in depth through two case studies on the coordination between Cuba and Venezuela, and between Russia and Iran.

Emergent social structure is typically not associated with survival in a facultatively social mammal

For social animals, group social structure has important consequences for disease and information spread. While prior studies showed individual connectedness within a group has fitness consequences, less is known about the fitness consequences of group social structure for the individuals who comprise the group. Using a long-term dataset on a wild population of facultatively social yellow-bellied marmots (Marmota flaviventer), we showed social structure had largely no relationship with survival, suggesting consequences of individual social phenotypes may not scale to the group social phenotype. An observed relationship for winter survival suggests a potentially contrasting direction of selection between the group and previous research on the individual level; less social individuals, but individuals in more social groups experience greater winter survival. This work provides valuable insights into evolutionary implications across social phenotypic scales.

Group social structure has limited impact on reproductive success in a wild mammal

The frequency and type of dyadic social interactions individuals partake in has important fitness consequences. Social network analysis is an effective tool to quantify the complexity and consequences of these behaviors on the individual level. Less work has used social networks to quantify the social structure—specific attributes of the pattern of all social interactions in a network—of animal social groups, and its fitness consequences for those individuals who comprise the group. We studied the association between social structure, quantified via five network measures, and annual reproductive success in wild, free-living female yellow-bellied marmots (Marmota flaviventer). We quantified reproductive success in two ways: (1) if an individual successfully weaned a litter and (2) how many pups were weaned. Networks were constructed from 38 968 interactions between 726 unique individuals in 137 social groups across 19 years. Using generalized linear mixed models, we found largely no relationship between either measure of reproductive success and social structure. We found a modest relationship that females residing in more fragmentable social groups (i.e., groups breakable into two or more separate groups of two or more individuals) weaned larger litters. Prior work showed that yellow-bellied marmots residing in more fragmentable groups gained body mass faster—another important fitness correlate. Interestingly, we found no strong relationships between other attributes of social group structure, suggesting that in this facultatively social mammal, the position of individuals within their group, the individual social phenotype, may be more important for fitness than the emergent group social phenotype.

The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area.

Bow-tie structures of twitter discursive communities

Bow-tie structures were introduced to describe the World Wide Web (WWW): in the direct network in which the nodes are the websites and the edges are the hyperlinks connecting them, the greatest number of nodes takes part to a bow-tie, i.e. a Weakly Connected Component (WCC) composed of 3 main sectors: IN, OUT and SCC. SCC is the main Strongly Connected Component of WCC, i.e. the greatest subgraph in which each node is reachable by any other one. The IN and OUT sectors are the set of nodes not included in SCC that, respectively, can access and are accessible to nodes in SCC. In the WWW, the greatest part of the websites can be found in the SCC, while the search engines belong to IN and the authorities, as Wikipedia, are in OUT. In the analysis of Twitter debate, the recent literature focused on discursive communities, i.e. clusters of accounts interacting among themselves via retweets. In the present work, we studied discursive communities in 8 different thematic Twitter datasets in various languages. Surprisingly, we observed that almost all discursive communities therein display a bow-tie structure during political or societal debates. Instead, they are absent when the argument of the discussion is different as sport events, as in the case of Euro2020 Turkish and Italian datasets. We furthermore analysed the quality of the content created in the various sectors of the different discursive communities, using the domain annotation from the fact-checking website Newsguard: we observe that, when the discursive community is affected by m/disinformation, the content with the lowest quality is the one produced and shared in SCC and, in particular, a strong incidence of low- or non-reputable messages is present in the flow of retweets between the SCC and the OUT sectors. In this sense, in discursive communities affected by m/disinformation, the greatest part of the accounts has access to a great variety of contents, but whose quality is, in general, quite low; such a situation perfectly describes the phenomenon of infodemic, i.e. the access to "an excessive amount of information about a problem, which makes it difficult to identify a solution", according to WHO.

A network analysis of connected biophysical pathways to advice eelgrass (Zostera marina) restoration

The North Sea and the Baltic Sea, including Danish coastal waters, have experienced a drastic decline in eelgrass Zostera marina coverage during the past century. Around 1900, eelgrass meadows covered about 6700 km² of Danish coastal waters while the current potential distribution area is only about one third of this. In some areas, the potential distribution area is far from realized, and restoration efforts are needed to assist recovery. Such efforts are challenging, and resource-demanding and careful site selection is, therefore, important. In the present study, we aim to identify the connectivity of eelgrass populations as a basis for guiding site selection for restoration. We developed a coupled biophysical model to study eelgrass dispersal in the Kattegat. Partly submerged particles simulated the dispersal of reproductive eelgrass shoots containing seeds during the flowering season July-September. We then used network analysis to identify the potential connectivity between populations. We evaluated connectivity based on In-strength, Betweenness and Eigenvector centrality metrics and identified key areas in the Kattegat such as the central part of Aalborg Bay, to be considered to restore the network of Z. marina patches. The study proves the potentials of combining hydrodynamic models and network analysis to support marine conservation and planning, and highlights the importance of collaboration between ecologists, oceanographers, and practitioners in this endeavour.

Marmot mass gain rates relate to their group’s social structure

Mass gain is an important fitness correlate for survival in highly seasonal species. Although many physiological, genetic, life history, and environmental factors can influence mass gain, more recent work suggests the specific nature of an individual’s own social relationships also influences mass gain. However, less is known about consequences of social structure for individuals. We studied the association between social structure, quantified via social network analysis, and annual mass gain in yellow-bellied marmots (Marmota flaviventer). Social networks were constructed from 31 738 social interactions between 671 individuals in 125 social groups from 2002 to 2018. Using a refined dataset of 1022 observations across 587 individuals in 81 social groups, we fitted linear mixed models to analyze the relationship between attributes of social structure and individual mass gain. We found that individuals residing in more connected and unbreakable social groups tended to gain proportionally less mass. However, these results were largely age-dependent. Adults, who form the core of marmot social groups, residing in more spread apart networks had greater mass gain than those in tighter networks. Yearlings, involved in a majority of social interactions, and those who resided in socially homogeneous and stable groups had greater mass gain. These results show how the structure of the social group an individual resides in may have consequences for a key fitness correlate. But, importantly, this relationship was age-dependent.

Modelling a multiplex brain network by local transfer entropy

This paper deals with the information transfer mechanisms underlying causal relations between brain regions under resting condition. fMRI images of a large set of healthy individuals from the 1000 Functional Connectomes Beijing Zang dataset have been considered and the causal information transfer among brain regions studied using Transfer Entropy concepts. Thus, we explored the influence of a set of states in two given regions at time t (A_t B_t.) over the state of one of them at a following time step (B_t+1) and could observe a series of time-dependent events corresponding to four kinds of interactions, or causal rules, pointing to (de)activation and turn off mechanisms and sharing some features with positive and negative functional connectivity. The functional architecture emerging from such rules was modelled by a directional multilayer network based upon four interaction matrices and a set of indexes describing the effects of the network structure in several dynamical processes. The statistical significance of the models produced by our approach was checked within the used database of homogeneous subjects and predicts a successful extension, in due course, to detect differences among clinical conditions and cognitive states.

Structure Characteristics and Influencing Factors of Cross-Border Electricity Trade: A Complex Network Perspective

Electricity is one of the most widely used forms of energy. However, environmental pollution from electricity generation and the mismatch between electricity supply and demand have long been bothering economies across the world. Under this background, cross-border electricity trade provides a new direction for sustainable development. Based on the complex network approach, this paper aims to explore the structural characteristics and evolution of cross-border electricity trade networks and to figure out the factors influencing the formation of the network by using the more advanced network analysis method—ERGM. The results show that: (1) The scale of the electricity trade network is expanding, but there are still many economies not involved. (2) The centrality of the network shifts from west to east. The level of internal electricity interconnection is high in Europe, and Asian countries’ coordination role in cross-border electricity trade networks is enhanced. (3) Cross-border electricity trade helps to reduce CO2 emissions, achieve renewable energy transformation, and reduce power supply and demand mismatch. Large gaps in GDP, electricity prices, industrial structure, geographical distance and institutional distance between economies are not conducive to form the cross-border trade network, while the common language is on the contrary.

Network analysis of internal migration in Croatia

Migration, and urbanization as its consequence, is among the most intricate political and scientific topics, predicted to have huge effects on human lives in the near future. Thus being said, previous works have mainly focused on international migration, and the research on internal migration outside of the US is scarce, and in the case of Europe—the ubiquitous center of migration affairs—only in its infancy. Observing migration between settlements, especially using network analysis indicators and models, can help to explain and predict migration, as well as urbanization originating from internal migration. We therefore conducted a network analysis of internal migration in Croatia, providing insights into the size of internal migration in population, and relative sizes between intra-settlement migration, inter-settlement migration and population. Through centrality analysis, we provide insights into hierarchy of importance, especially, in terms of the overall flow and overall attractiveness of particular settlements in the network. The analysis of the network structure reveals high presence of reciprocity and thus the importance of internal migration to urbanization, as well as the systematic abandonment of large cities in the east of the country. The application of three different community detection algorithms provides insights for the policy domain in terms of the compatibility of the current country administrative subdivision schemes and the subdivision implied by migration patterns. For network scholars, the analysis at hand reveals the status quo in applied network analysis to migration, the works published, the measures used, and potential metrics outside those applied which may be used to better explain and predict the intricate phenomenon of human migration.

Dissecting molecular network structures using a network subgraph approach

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.

Complete Connectomic Reconstruction of Olfactory Projection Neurons in the Fly Brain

Nervous systems contain sensory neurons, local neurons, projection neurons, and motor neurons. To understand how these building blocks form whole circuits, we must distil these broad classes into neuronal cell types and describe their network connectivity. Using an electron micrograph dataset for an entire Drosophila melanogaster brain, we reconstruct the first complete inventory of olfactory projections connecting the antennal lobe, the insect analog of the mammalian olfactory bulb, to higher-order brain regions in an adult animal brain. We then connect this inventory to extant data in the literature, providing synaptic-resolution "holotypes" both for heavily investigated and previously unknown cell types. Projection neurons are approximately twice as numerous as reported by light level studies; cell types are stereotyped, but not identical, in cell and synapse numbers between brain hemispheres. The lateral horn, the insect analog of the mammalian cortical amygdala, is the main target for this olfactory information and has been shown to guide innate behavior. Here, we find new connectivity motifs, including axo-axonic connectivity between projection neurons, feedback, and lateral inhibition of these axons by a large population of neurons, and the convergence of different inputs, including non-olfactory inputs and memory-related feedback onto third-order olfactory neurons. These features are less prominent in the mushroom body calyx, the insect analog of the mammalian piriform cortex and a center for associative memory. Our work provides a complete neuroanatomical platform for future studies of the adult Drosophila olfactory system.

Average trapping time on weighted directed Koch network

Numerous recent studies have focused on random walks on undirected binary scale-free networks. However, random walks with a given target node on weighted directed networks remain less understood. In this paper, we first introduce directed weighted Koch networks, in which any pair of nodes is linked by two edges with opposite directions, and weights of edges are controlled by a parameter θ . Then, to evaluate the transportation efficiency of random walk, we derive an exact solution for the average trapping time (ATT), which agrees well with the corresponding numerical solution. We show that leading behaviour of ATT is function of the weight parameter θ and that the ATT can grow sub-linearly, linearly and super-linearly with varying θ . Finally, we introduce a delay parameter p to modify the transition probability of random walk, and provide a closed-form solution for ATT, which still coincides with numerical solution. We show that in the closed-form solution, the delay parameter p can change the coefficient of ATT, but cannot change the leading behavior. We also show that desired ATT or trapping efficiency can be obtained by setting appropriate weight parameter and delay parameter simultaneously. Thereby, this work advance the understanding of random walks on directed weighted scale-free networks.

Inference of the kinetic Ising model with heterogeneous missing data

We consider the problem of inferring a causality structure from multiple binary time series by using the kinetic Ising model in datasets where a fraction of observations is missing. Inspired by recent work on mean field methods for the inference of the model with hidden spins, we develop a pseudo-expectation-maximization algorithm that is able to work even in conditions of severe data sparsity. The methodology relies on the Martin-Siggia-Rose path integral method with second-order saddle-point solution to make it possible to approximate the log-likelihood in polynomial time, giving as output an estimate of the couplings matrix and of the missing observations. We also propose a recursive version of the algorithm, where at every iteration some missing values are substituted by their maximum-likelihood estimate, showing that the method can be used together with sparsification schemes such as lasso regularization or decimation. We test the performance of the algorithm on synthetic data and find interesting properties regarding the dependency on heterogeneity of the observation frequency of spins and when some of the hypotheses that are necessary to the saddle-point approximation are violated, such as the small couplings limit and the assumption of statistical independence between couplings.

Evidence to support common application switching behaviour on smartphones

We find evidence to support common behaviour in smartphone usage based on analysis of application (app) switching. This is an overlooked aspect of smartphone usage that gives additional insight beyond screen time and the particular apps that are accessed. Using a dataset of usage behaviour from 53 participants over a six-week period, we find strong similarity in the structure of networks built from app switching, despite diversity in the apps used, and the volume of app switching. App switch networks exhibit small-world, broad-scale network features, with a rapid popularity decay, suggesting that preferential attachment may drive next-app decision-making.

Structure and dynamical behavior of non-normal networks

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.

Dynamics of collective performance in collaboration networks

Today, many complex tasks are assigned to teams, rather than individuals. One reason for teaming up is expansion of the skill coverage of each individual to the joint team skill set. However, numerous empirical studies of human groups suggest that the performance of equally skilled teams can widely differ. Two natural question arise: What are the factors defining team performance? and How can we best predict the performance of a given team on a specific task? While the team members’ task-related capabilities constrain the potential for the team’s success, the key to understanding team performance is in the analysis of the team process, encompassing the behaviors of the team members during task completion. In this study, we extend the existing body of research on team process and prediction models of team performance. Specifically, we analyze the dynamics of historical team performance over a series of tasks as well as the fine-grained patterns of collaboration between team members, and formally connect these dynamics to the team performance in the predictive models. Our major qualitative finding is that higher performing teams have well-connected collaboration networks—as indicated by the topological and spectral properties of the latter—which are more robust to perturbations, and where network processes spread more efficiently. Our major quantitative finding is that our predictive models deliver accurate team performance predictions—with a prediction error of 15-25%—on a variety of simple tasks, outperforming baseline models that do not capture the micro-level dynamics of team member behaviors. We also show how to use our models in an application, for optimal online planning of workload distribution in an organization. Our findings emphasize the importance of studying the dynamics of team collaboration as the major driver of high performance in teams.

Using Social Network Analysis to Investigate Positive EOL Communication

CONTEXT

End-of-life (EOL) communication is a complex process involving the whole family and multiple care providers. Applications of analysis techniques that account for communication beyond the patient and patient/provider will improve clinical understanding of EOL communication.

OBJECTIVES

The objectives of the study were to introduce the use of social network analysis to EOL communication data and to provide an example of applying social network analysis to home hospice interactions.

METHODS

We provide a description of social network analysis to model communication patterns during home hospice nursing visits. We describe three social network attributes (i.e., magnitude, directionality, and reciprocity) in the expression of positive emotion among hospice nurses, family caregivers, and hospice cancer patients. Differences in communication structure by primary family caregiver across gender and time were also examined.

RESULTS

Magnitude (frequency) in the expression of positive emotion occurred most often between nurses and caregivers or between nurses and patients. Female caregivers directed more positive emotion to nurses, and nurses directed more positive emotion to other family caregivers when the primary family caregiver was male. Reciprocity (mutuality) in positive emotion declined toward day of death but increased on day of actual patient death. There was a variation in reciprocity by the type of positive emotion expressed.

CONCLUSION

Our example demonstrates that social network analysis can be used to better understand the process of EOL communication. Social network analysis can be expanded to other areas of EOL research, such as EOL decision making and health care teamwork.

Do learning collaboratives strengthen communication? A comparison of organizational team communication networks over time

BACKGROUND

Collaborative learning models were designed to support quality improvements, such as innovation implementation by promoting communication within organizational teams. Yet the effect of collaborative learning approaches on organizational team communication during implementation is untested.

PURPOSE

The aim of this study was to explore change in communication patterns within teams from children's mental health organizations during a year-long learning collaborative focused on implementing a new treatment. We adopt a social network perspective to examine intraorganizational communication within each team and assess change in (a) the frequency of communication among team members, (b) communication across organizational hierarchies, and (c) the overall structure of team communication networks.

METHODOLOGY/APPROACH

A pretest-posttest design compared communication among 135 participants from 21 organizational teams at the start and end of a learning collaborative. At both time points, participants were asked to list the members of their team and rate the frequency of communication with each along a 7-point Likert scale. Several individual, pair-wise, and team level communication network metrics were calculated and compared over time.

FINDINGS

At the individual level, participants reported communicating with more team members by the end of the learning collaborative. Cross-hierarchical communication did not change. At the team level, these changes manifested differently depending on team size. In large teams, communication frequency increased, and networks grew denser and slightly less centralized. In small teams, communication frequency declined, growing more sparse and centralized.

PRACTICE IMPLICATIONS

Results suggest that team communication patterns change minimally but evolve differently depending on size. Learning collaboratives may be more helpful for enhancing communication among larger teams; thus, managers might consider selecting and sending larger staff teams to learning collaboratives. This study highlights key future research directions that can disentangle the relationship between learning collaboratives and team networks.

Stability of centrality measures in valued networks regarding different actor non-response treatments and macro-network structures

Social network data are prone to errors regardless their source. This paper focuses on missing data due to actor non-response in valued networks. If actors refuse to provide information, all values for outgoing ties are missing. Partially observed incoming ties to non-respondents and all other patterns for ties between members of the network can be used to impute missing outgoing ties. Many centrality measures are used to determine the most prominent actors inside the network. Using treatments for actor non-response enables us to estimate better the centrality scores of all actors regarding their popularity or prominence. Simulations using initial known blockmodel structures based on three most frequently occurring macro-network structures: cohesive subgroups, core-periphery models, and hierarchical structures were used to evaluate the relative merits of the treatments for non-response. The results indicate that the amount of non-respondents, the type of underlying macro-structure, and the employed treatment have an impact on centrality scores. Regardless of the underlying network structure, the median of the 3-nearest neighbors based on incoming ties performs the best. The adequacy (or not) of the other non-response treatments is contingent on the network macro-structure.

Structural and functional, empirical and modeled connectivity in the cerebral cortex of the rat

Connectomics data from animal models provide an invaluable opportunity to reveal the complex interplay between structure and function in the mammalian brain. In this work, we investigate the relationship between structural and functional connectivity in the rat brain cortex using a directed anatomical network generated from a carefully curated meta-analysis of published tracing data, along with resting-state functional MRI data obtained from a group of 14 anesthetized Wistar rats. We found a high correspondence between the strength of functional connections, measured as blood oxygen level dependent (BOLD) signal correlations between cortical regions, and the weight of the corresponding anatomical links in the connectome graph (maximum Spearman rank-order correlation ρ=0.48). At the network-level, regions belonging to the same functionally defined community tend to form more mutual weighted connections between each other compared to regions located in different communities. We further found that functional communities in resting-state networks are enriched in densely connected anatomical motifs. Importantly, these higher-order structural subgraphs cannot be explained by lower-order topological properties, suggesting that dense structural patterns support functional associations in the resting brain. Simulations of brain-wide resting-state activity based on neural mass models implemented on the empirical rat anatomical connectome demonstrated high correlation between the simulated and the measured functional connectivity (maximum Pearson correlation ρ=0.53), further suggesting that the topology of structural connections plays an important role in shaping functional cortical networks.

The effect of social connections on the discovery of multiple hidden food patches in a bird species

Social foraging is thought to provide the possibility of information transmission between individuals, but this advantage has been proved only in a handful of species and contexts. We investigated how social connections in captive flocks of house sparrows (Passer domesticus) affected the discovery of (i.e. feeding for the first time from) two hidden food patches in the presence of informed flock-mates. At the first-discovered and most-exploited food patch social connections between birds affected the order of discovery and presumably contributed to a greater exploitation of this patch. However, social connections did not affect discovery at the second food patch despite its close spatial proximity. Males discovered the food sources sooner than females, while feeding activity was negatively related to patch discovery. Age had no effect on the order of discovery. Birds that first discovered and fed at the food patches were characterized by higher level of social indifference, i.e. followed others less frequently than other birds in an independent context. Our findings provide experimental evidence for the importance of variable social connections during social foraging in house sparrow flocks, and suggest that social attraction can contribute differently to the exploitation of different patches when multiple food sources are present.

Multiplexity and multireciprocity in directed multiplexes

Real-world multilayer networks feature nontrivial dependencies among links of different layers. Here we argue that if links are directed, then dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of "multiplexity," there is also a tendency to antialign as a result of what we call "multireciprocity," i.e., the fact that links in one layer can be reciprocated by opposite links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the world trade multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is, however, largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow us to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness and complexity metrics.

Network architecture of the cerebral nuclei (basal ganglia) association and commissural connectome

The cerebral nuclei form the ventral division of the cerebral hemisphere and are thought to play an important role in neural systems controlling somatic movement and motivation. Network analysis was used to define global architectural features of intrinsic cerebral nuclei circuitry in one hemisphere (association connections) and between hemispheres (commissural connections). The analysis was based on more than 4,000 reports of histologically defined axonal connections involving all 45 gray matter regions of the rat cerebral nuclei and revealed the existence of four asymmetrically interconnected modules. The modules form four topographically distinct longitudinal columns that only partly correspond to previous interpretations of cerebral nuclei structure-function organization. The network of connections within and between modules in one hemisphere or the other is quite dense (about 40% of all possible connections), whereas the network of connections between hemispheres is weak and sparse (only about 5% of all possible connections). Particularly highly interconnected regions (rich club and hubs within it) form a topologically continuous band extending through two of the modules. Connection path lengths among numerous pairs of regions, and among some of the network's modules, are relatively long, thus accounting for low global efficiency in network communication. These results provide a starting point for reexamining the connectional organization of the cerebral hemispheres as a whole (right and left cerebral cortex and cerebral nuclei together) and their relation to the rest of the nervous system.

Spatio-temporal networks: reachability, centrality and robustness

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. To identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting spatio-temporally efficient flows through the network. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attacks.

Interactions between Financial and Environmental Networks in OECD Countries

We analysed a multiplex of financial and environmental networks between OECD countries from 2002 to 2010. Foreign direct investments and portfolio investment showing the flows in equity securities, short-term, long-term and total debt, these securities represent the financial layers; emissions of NOx, PM10, SO2, CO2 equivalent and the water footprint associated with international trade represent the environmental layers. We present a new measure of cross-layer correlations between flows in different layers based on reciprocity. For the assessment of results, we implement a null model for this measure based on the exponential random graph theory. We find that short-term financial flows are more correlated with environmental flows than long-term investments. Moreover, the correlations between reverse financial and environmental flows (i.e. the flows of different layers going in opposite directions) are generally stronger than correlations between synergic flows (flows going in the same direction). This suggests a trade-off between financial and environmental layers, where, more financialised countries display higher correlations between outgoing financial flows and incoming environmental flows than from lower financialised countries. Five countries are identified as hubs in this finance-environment multiplex: The United States, France, Germany, Belgium-Luxembourg and United Kingdom.

Multiplexity versus correlation: the role of local constraints in real multiplexes

Several systems can be represented as multiplex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical quantities aiming at capturing the added level of complexity of those systems is required. Various steps in this direction have been made. In the simplest case, dependencies between layers are measured via correlation-based metrics, a procedure that we show to be equivalent to the use of completely homogeneous benchmarks specifying only global constraints. However, this approach does not take into account the heterogeneity in the degree and strength distributions, which is instead a fundamental feature of real-world multiplexes. In this work, we compare the observed dependencies between layers with the expected values obtained from maximum-entropy reference models that appropriately control for the observed heterogeneity in the degree and strength distributions. This information-theoretic approach results in the introduction of novel and improved multiplexity measures that we test on different datasets, i.e. the International Trade Network and the European Airport Network. Our findings confirm that the use of homogeneous benchmarks can lead to misleading results, and highlight the important role played by the distribution of hubs across layers.

Effects of reciprocity on random walks in weighted networks

It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted network with a trap at the central hub node, where the weight of each directed edge is dominated by a parameter controlling the extent of network reciprocity. We derive two expressions for the mean first passage time (MFPT) to the trap, by using two different techniques, the results of which agree well with each other. We also analytically determine all the eigenvalues as well as their multiplicities for the fundamental matrix of the dynamical process, and show that the largest eigenvalue has an identical dominant scaling as that of the MFPT.We find that the weight parameter has a substantial effect on the MFPT, which behaves as a power-law function of the system size with the power exponent dependent on the parameter, signaling the crucial role of reciprocity in random walks occurring in weighted networks.

Reconstructing the world trade multiplex: the role of intensive and extensive biases

In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown. However, several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths. Here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node. We study several temporal snapshots and almost 100 layers (commodity classes) of the multiplex and find that the observed properties are systematically well reproduced by our model. Our formalism allows us to introduce the (static) concept of extensive and intensive bias, defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights, with respect to a reference case where only strengths are enforced. Our findings complement the existing economic literature on (dynamic) intensive and extensive trade margins. More generally, they show that real-world multiplexes can be strongly shaped by layer-specific local constraints.