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Concept: Random graph


Weight-based stigma compromises the social networks of overweight children. To date, research on the position of overweight children in their peer network has focused only on friendship relations, and not on negative relationship dimensions. This study examined how overweight was associated with relations of friendship and dislike (antipathies) in the peer group. Exponential random graph models (ERGM) were used to examine friendship and antipathy relations among overweight children and their classmates, using a sub-sample from the TRacking Adolescents' Individual Lives Survey (N = 504, M age 11.4). Findings showed that overweight children were less likely to receive friendship nominations, and were more likely to receive dislike nominations. Overweight children were also more likely than their non-overweight peers to nominate classmates that they disliked. Together, the results indicate that positive and negative peer relations are impacted by children’s weight status, and are relevant to addressing the social marginalization of overweight children.

Concepts: Sociology, Adolescence, Graph theory, Peer group, Friendship, Peer-to-peer, Network theory, Random graph


Live pig trade patterns, drivers and characteristics, particularly in backyard predominant systems, remain largely unexplored despite their important contribution to the spread of infectious diseases in the swine industry. A better understanding of the pig trade dynamics can inform the implementation of risk-based and more cost-effective prevention and control programs for swine diseases. In this study, a semi-structured questionnaire elaborated by FAO and implemented to 487 farmers was used to collect data regarding basic characteristics about pig demographics and live-pig trade among villages in the country of Georgia, where very scarce information is available. Social network analysis and exponential random graph models were used to better understand the structure, contact patterns and main drivers for pig trade in the country. Results indicate relatively infrequent (a total of 599 shipments in one year) and geographically localized (median Euclidean distance between shipments = 6.08 km; IQR = 0-13.88 km) pig movements in the studied regions. The main factors contributing to live-pig trade movements among villages were being from the same region (i.e., local trade), usage of a middleman or a live animal market to trade live pigs by at least one farmer in the village, and having a large number of pig farmers in the village. The identified villages' characteristics and structural network properties could be used to inform the design of more cost-effective surveillance systems in a country which pig industry was recently devastated by African swine fever epidemics and where backyard production systems are predominant.

Concepts: Epidemiology, Infectious disease, Influenza, Pig, Social network, Network theory, Surveillance, Random graph


We study the cohesion within and the coalitions between political groups in the Eighth European Parliament (2014-2019) by analyzing two entirely different aspects of the behavior of the Members of the European Parliament (MEPs) in the policy-making processes. On one hand, we analyze their co-voting patterns and, on the other, their retweeting behavior. We make use of two diverse datasets in the analysis. The first one is the roll-call vote dataset, where cohesion is regarded as the tendency to co-vote within a group, and a coalition is formed when the members of several groups exhibit a high degree of co-voting agreement on a subject. The second dataset comes from Twitter; it captures the retweeting (i.e., endorsing) behavior of the MEPs and implies cohesion (retweets within the same group) and coalitions (retweets between groups) from a completely different perspective. We employ two different methodologies to analyze the cohesion and coalitions. The first one is based on Krippendorff’s Alpha reliability, used to measure the agreement between raters in data-analysis scenarios, and the second one is based on Exponential Random Graph Models, often used in social-network analysis. We give general insights into the cohesion of political groups in the European Parliament, explore whether coalitions are formed in the same way for different policy areas, and examine to what degree the retweeting behavior of MEPs corresponds to their co-voting patterns. A novel and interesting aspect of our work is the relationship between the co-voting and retweeting patterns.

Concepts: European Union, Treaty of Lisbon, European Parliament, Member of Parliament, Member of the European Parliament, Random graph, Coalition government, European Parliament election, 2009


Understanding the network structure of long distance pathways in the brain is a necessary step towards developing an insight into the brain’s function, organization and evolution. Dense global subnetworks of these pathways have often been studied, primarily due to their functional implications. Instead we study sparse local subnetworks of the pathways to establish the role of a brain area in enabling shortest path communication between its non-adjacent topological neighbours. We propose a novel metric to measure the topological communication load on a vertex due to its immediate neighbourhood, and show that in terms of distribution of this local communication load, a network of Macaque long distance pathways is substantially different from other real world networks and random graph models. Macaque network contains the entire range of local subnetworks, from star-like networks to clique-like networks, while other networks tend to contain a relatively small range of subnetworks. Further, sparse local subnetworks in the Macaque network are not only found across topographical super-areas, e.g., lobes, but also within a super-area, arguing that there is conservation of even relatively short-distance pathways. To establish the communication role of a vertex we borrow the concept of brokerage from social science, and present the different types of brokerage roles that brain areas play, highlighting that not only the thalamus, but also cingulate gyrus and insula often act as “relays” for areas in the neocortex. These and other analysis of communication load and roles of the sparse subnetworks of the Macaque brain provide new insights into the organisation of its pathways.

Concepts: Neuroanatomy, Brain, Cerebral cortex, Cerebrum, Graph theory, Shortest path problem, Cingulate gyrus, Random graph


We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.

Concepts: Natural selection, Evolution, Graph theory, Population genetics, Individual, Genetic drift, Random graph, Alfréd Rényi


Academic collaboration is critical to knowledge production, especially as teams dominate scientific endeavors. Typical predictors of collaboration include individual characteristics such as academic rank or institution, and network characteristics such as a central position in a publication network. The role of disciplinary affiliation in the initiation of an academic collaboration between two investigators deserves more attention. Here, we examine the influence of disciplinary patterns on collaboration formation with control of known predictors using an inferential network model. The study group included all researchers in the Institute of Clinical and Translational Sciences (ICTS) at Washington University in St. Louis. Longitudinal data were collected on co-authorships in grants and publications before and after ICTS establishment. Exponential-family random graph models were used to build the network models. The results show that disciplinary affiliation independently predicted collaboration in grant and publication networks, particularly in the later years. Overall collaboration increased in the post-ICTS networks, with cross-discipline ties occurring more often than within-discipline ties in grants, but not publications. This research may inform better evaluation models of university-based collaboration, and offer a roadmap to improve cross-disciplinary collaboration with discipline-informed network interventions.

Concepts: Scientific method, Sociology, Academic publishing, Science, Research, Graph theory, Knowledge, Random graph


We study the network dismantling problem, which consists of determining a minimal set of vertices in which removal leaves the network broken into connected components of subextensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices, leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading, we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective, we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide additional insights into the dismantling problem, concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well-performing nodes.

Concepts: Mathematics, The Network, Graph theory, Mechanics, Graph, Planar graph, Random graph, Alfréd Rényi


The interaction of positive and negative relationships (i.e. I like you, but you dislike me - referred to as relational dissonance) is an underexplored phenomenon. Further, it is often only poor (or negative) mental health that is examined in relation to social networks, with little regard for positive psychological wellbeing. Finally, these issues are compounded by methodological constraints. This study explores a new concept of relational dissonance alongside mutual antipathies and friendships and their association with mental health using multivariate exponential random graph models with an Australian sample of secondary school students. Results show male students with relationally dissonant ties have lower positive mental health measures. Girls with relationally dissonant ties have lower depressed mood, but those girls being targeted by negative ties are more likely to have depressed mood. These findings have implications for the development of interventions focused on promoting adolescent wellbeing and consideration of the appropriate measurement of wellbeing and mental illness.

Concepts: Psychology, Mental health, Sociology, Illness, Interpersonal relationship, Bipolar disorder, Secondary education, Random graph


The aim of this research was to investigate the interplay between victim-aggressor relationships and defending relationships in early childhood to test the proposition that young aggressors are less selective than older children in their choice of vulnerable targets. Cross-sectional multivariate statistical social network analyses (Exponential Random Graph Models) for a sample of 177 preschoolers from seven classes, 5- to 7-years-old, revealed that boys were more aggressive than girls, toward both boys and girls, whereas defending relationships were most often same-sex. There was significant reciprocity in aggression, indicating that it was more often bidirectional rather than unidirectional. In addition, aggressors clearly defended each other when they shared their targets of aggression, whereas a marginally significant trend appeared for defending between victims who were victimized by the same aggressors. Furthermore, teacher-rated dominance was positively associated with children’s involvement in both aggression and victimization, and teacher-rated insecurity was associated with less aggression, but not with victimization. These findings suggest that those who are reported as being victimized may retaliate, or be aggressive themselves, and do not display some of the vulnerabilities reported among older groups of victims. The findings are in line with the proposition that young aggressors are less strategic than older children in targeting vulnerable victims. The network approach to peer victimization and defending contributes to understanding the social processes facilitating the development of aggression in early childhood.

Concepts: Sociology, Childhood, Aggression, Social psychology, Social network, Network theory, Random graph


We demonstrate a general method to analyze the sensitivity of attack rate in a network model of infectious disease epidemiology to the structure of the network. We use Moore and Shannon’s “network reliability” statistic to measure the epidemic potential of a network. A number of networks are generated using exponential random graph models based on the properties of the contact network structure of one of the Add Health surveys. The expected number of infections on the original Add Health network is significantly different from that on any of the models derived from it. Because individual-level transmissibility and network structure are not separately identifiable parameters given population-level attack rate data it is possible to re-calibrate the transmissibility to fix this difference. However, the temporal behavior of the outbreak remains significantly different. Hence any estimates of the effectiveness of time dependent interventions on one network are unlikely to generalize to the other. Moreover, we show that in one case even a small perturbation to the network spoils the re-calibration. Unfortunately, the set of sufficient statistics for specifying a contact network model is not yet known. Until it is, estimates of the outcome of a dynamical process on a particular network obtained from simulations on a different network are not reliable.

Concepts: Epidemiology, Infectious disease, Estimator, Infection, Probability theory, Graph theory, Expected value, Random graph