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Concept: Centrality


Whilst being hailed as the remedy to the world’s ills, cities will need to adapt in the 21(st) century. In particular, the role of public transport is likely to increase significantly, and new methods and technics to better plan transit systems are in dire need. This paper examines one fundamental aspect of transit: network centrality. By applying the notion of betweenness centrality to 28 worldwide metro systems, the main goal of this paper is to study the emergence of global trends in the evolution of centrality with network size and examine several individual systems in more detail. Betweenness was notably found to consistently become more evenly distributed with size (i.e. no “winner takes all”) unlike other complex network properties. Two distinct regimes were also observed that are representative of their structure. Moreover, the share of betweenness was found to decrease in a power law with size (with exponent 1 for the average node), but the share of most central nodes decreases much slower than least central nodes (0.87 vs. 2.48). Finally the betweenness of individual stations in several systems were examined, which can be useful to locate stations where passengers can be redistributed to relieve pressure from overcrowded stations. Overall, this study offers significant insights that can help planners in their task to design the systems of tomorrow, and similar undertakings can easily be imagined to other urban infrastructure systems (e.g., electricity grid, water/wastewater system, etc.) to develop more sustainable cities.

Concepts: Central America, The Remedy, Train station, Public transport, Social network, Complex system, City, Centrality


A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Concepts: Computational complexity theory, Networks, Real number, Algorithm, Network topology, Social network, Graph theory, Centrality


Lice are socially-transmitted ectoparasites. Transmission depends upon their host’s degree of contact with conspecifics. While grooming facilitates ectoparasite transmission via body contact, it also constrains their spread through parasite removal. We investigated relations between parasite burden and sociality in female Japanese macaques following two opposing predictions: i) central females in contact/grooming networks harbour more lice, related to their numerous contacts; ii) central females harbour fewer lice, related to receiving more grooming. We estimated lice load non-invasively using the conspicuous louse egg-picking behaviour performed by macaques during grooming. We tested for covariation in several centrality measures and lice load, controlling for season, female reproductive state and dominance rank. Results show that the interaction between degree centrality (number of partners) and seasonality predicted lice load: females interacting with more partners had fewer lice than those interacting with fewer partners in winter and summer, whereas there was no relationship between lice load and centrality in spring and fall. This is counter to the prediction that increased contact leads to greater louse burden but fits the prediction that social grooming limits louse burden. Interactions between environmental seasonality and both parasite and host biology appeared to mediate the role of social processes in louse burden.

Concepts: Primate, Interaction, Parasitism, Prophecy, Futurology, Centrality, Prediction


Understanding how youth football players base their game interactions may constitute a solid criterion for fine-tuning the training process and, ultimately, to achieve better individual and team performances during competition. The present study aims to explore how passing networks and positioning variables can be linked to the match outcome in youth elite association football. The participants included 44 male elite players from under-15 and under-17 age groups. A passing network approach within positioning-derived variables was computed to identify the contributions of individual players for the overall team behaviour outcome during a simulated match. Results suggested that lower team passing dependency for a given player (expressed by lower betweenness network centrality scores) and high intra-team well-connected passing relations (expressed by higher closeness network centrality scores) were related to better outcomes. The correlation between the dyads' positioning regularity and the passing density showed a most likely higher correlation in under-15 (moderate effect), indicating a possible more dependence of the ball position rather than in the under-17 teams (small/unclear effects). Overall, this study emphasizes the potential of coupling notational analyses with spatial-temporal relations to produce a more functional and holistic understanding of teams' sports performance. Also, the social network analysis allowed to reveal novel key determinants of collective performance.

Concepts: Network science, Network theory, Football, Sociology, Game theory, Networks, Centrality, Social network


To the authors' knowledge, social network status in adolescent and young adult (AYA) cancer survivors has not been adequately studied to date. The authors developed and validated a functional social network index (FSNI) for AYA survivors, and compared its performance with that of 2 traditional indices (density and betweenness centrality).

Concepts: Index, Networks, Adolescence, Sociology, Social network, Centrality


Alzheimer’s disease and progressive supranuclear palsy (PSP) represent neurodegenerative tauopathies with predominantly cortical versus subcortical disease burden. In Alzheimer’s disease, neuropathology and atrophy preferentially affect ‘hub’ brain regions that are densely connected. It was unclear whether hubs are differentially affected by neurodegeneration because they are more likely to receive pathological proteins that propagate trans-neuronally, in a prion-like manner, or whether they are selectively vulnerable due to a lack of local trophic factors, higher metabolic demands, or differential gene expression. We assessed the relationship between tau burden and brain functional connectivity, by combining in vivo PET imaging using the ligand AV-1451, and graph theoretic measures of resting state functional MRI in 17 patients with Alzheimer’s disease, 17 patients with PSP, and 12 controls. Strongly connected nodes displayed more tau pathology in Alzheimer’s disease, independently of intrinsic connectivity network, validating the predictions of theories of trans-neuronal spread but not supporting a role for metabolic demands or deficient trophic support in tau accumulation. This was not a compensatory phenomenon, as the functional consequence of increasing tau burden in Alzheimer’s disease was a progressive weakening of the connectivity of these same nodes, reducing weighted degree and local efficiency and resulting in weaker ‘small-world’ properties. Conversely, in PSP, unlike in Alzheimer’s disease, those nodes that accrued pathological tau were those that displayed graph metric properties associated with increased metabolic demand and a lack of trophic support rather than strong functional connectivity. Together, these findings go some way towards explaining why Alzheimer’s disease affects large scale connectivity networks throughout cortex while neuropathology in PSP is concentrated in a small number of subcortical structures. Further, we demonstrate that in PSP increasing tau burden in midbrain and deep nuclei was associated with strengthened cortico-cortical functional connectivity. Disrupted cortico-subcortical and cortico-brainstem interactions meant that information transfer took less direct paths, passing through a larger number of cortical nodes, reducing closeness centrality and eigenvector centrality in PSP, while increasing weighted degree, clustering, betweenness centrality and local efficiency. Our results have wide-ranging implications, from the validation of models of tau trafficking in humans to understanding the relationship between regional tau burden and brain functional reorganization.

Concepts: Positron emission tomography, Graph theory, Distance, Tau protein, Alzheimer's disease, Centrality, Tauopathy, Neurodegenerative disorders


Information flow during catastrophic events is a critical aspect of disaster management. Modern communication platforms, in particular online social networks, provide an opportunity to study such flow and derive early-warning sensors, thus improving emergency preparedness and response. Performance of the social networks sensor method, based on topological and behavioral properties derived from the “friendship paradox”, is studied here for over 50 million Twitter messages posted before, during, and after Hurricane Sandy. We find that differences in users' network centrality effectively translate into moderate awareness advantage (up to 26 hours); and that geo-location of users within or outside of the hurricane-affected area plays a significant role in determining the scale of such an advantage. Emotional response appears to be universal regardless of the position in the network topology, and displays characteristic, easily detectable patterns, opening a possibility to implement a simple “sentiment sensing” technique that can detect and locate disasters.

Concepts: Emergency management, Network theory, Graph theory, Centrality, Network topology, Networks, Sociology, Social network


Centrality measures such as the degree, k-shell, or eigenvalue centrality can identify a network’s most influential nodes, but are rarely usefully accurate in quantifying the spreading power of the vast majority of nodes which are not highly influential. The spreading power of all network nodes is better explained by considering, from a continuous-time epidemiological perspective, the distribution of the force of infection each node generates. The resulting metric, the expected force, accurately quantifies node spreading power under all primary epidemiological models across a wide range of archetypical human contact networks. When node power is low, influence is a function of neighbor degree. As power increases, a node’s own degree becomes more important. The strength of this relationship is modulated by network structure, being more pronounced in narrow, dense networks typical of social networking and weakening in broader, looser association networks such as the Internet. The expected force can be computed independently for individual nodes, making it applicable for networks whose adjacency matrix is dynamic, not well specified, or overwhelmingly large.

Concepts: Centrality, Torque, Networks, Epidemiology, Graph theory, Computer network, Fundamental physics concepts, Social network


Individuals' centrality in their social network (who they and their social ties are connected to) has been associated with fertility, longevity, disease and information transmission in a range of taxa. Here, we present the first exploration in humans of the relationship between reproductive success and different measures of network centrality of 39 Agta and 38 BaYaka mothers. We collected three-meter contact (‘proximity’) networks and reproductive histories to test the prediction that individual centrality is positively associated with reproductive fitness (number of living offspring). Rather than direct social ties influencing reproductive success, mothers with greater indirect centrality (i.e. centrality determined by second and third degree ties) produced significantly more living offspring. However, indirect centrality is also correlated with sickness in the Agta, suggesting a trade-off. In complex social species, the optimisation of individuals' network position has important ramifications for fitness, potentially due to easy access to different parts of the network, facilitating cooperation and social influence in unpredictable ecologies.

Concepts: Complex network, Mathematical sociology, Network theory, Reproductive success, Centrality, Social network, Networks, Sociology


The potential for academic research institutions to facilitate knowledge exchange and influence evidence-informed decision-making has been gaining ground. Schools of public health (SPHs) may play a key knowledge brokering role-serving as agencies of and for development. Understanding academic-policymaker networks can facilitate the enhancement of links between policymakers and academic faculty at SPHs, as well as assist in identifying academic knowledge brokers (KBs). Using a census approach, we administered a sociometric survey to academic faculty across six SPHs in Kenya to construct academic-policymaker networks. We identified academic KBs using social network analysis (SNA) in a two-step approach: First, we ranked individuals based on (1) number of policymakers in their network; (2) number of academic peers who report seeking them out for advice on knowledge translation and (3) their network position as ‘inter-group connectors’. Second, we triangulated the three scores and re-ranked individuals. Academic faculty scoring within the top decile across all three measures were classified as KBs. Results indicate that each SPH commands a variety of unique as well as overlapping relationships with national ministries in Kenya. Of 124 full-time faculty, we identified 7 KBs in 4 of the 6 SPHs. Those scoring high on the first measure were not necessarily the same individuals scoring high on the second. KBs were also situated in a wide range along the ‘connector/betweenness’ measure. We propose that a composite score rather than traditional ‘betweenness centrality’, provides an alternative means of identifying KBs within these networks. In conclusion, SNA is a valuable tool for identifying academic-policymaker networks in Kenya. More efforts to conduct similar network studies would permit SPH leadership to identify existing linkages between faculty and policymakers, shared linkages with other SPHs and gaps so as to contribute to evidence-informed health policies.

Concepts: University, Network theory, Centrality, College, Networks, Knowledge management, Academia, Social network