Collective dynamics of 'small-world' networks

Watts, Duncan J.; Strogatz, Steven H.

doi:10.1515/9781400841356.301

Cited by 5,935 publications

(9,577 citation statements)

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“…Most relevant for neuroscience and the connectome are networks measures that evaluate the degree of clustering and modularity (measures of functional segregation), and of path length and communication efficiency (measures of functional integration). In a seminal study (Watts and Strogatz, 1998) discovered that networks combining high clustering of local connections and a short path length due to a small fraction of long-range connections were organized as a "smallworld". In such networks, any node can be reached from any other node in a small number of steps, despite the fact that most nodes form tightly coupled local communities.…”

Section: Brain Structural Network Analysismentioning

confidence: 99%

MR connectomics: Principles and challenges

Hagmann

Cammoun

Gigandet

et al. 2010

Journal of Neuroscience Methods

256

207

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a b s t r a c t MR connectomics is an emerging framework in neuro-science that combines diffusion MRI and whole brain tractography methodologies with the analytical tools of network science. In the present work we review the current methods enabling structural connectivity mapping with MRI and show how such data can be used to infer new information of both brain structure and function. We also list the technical challenges that should be addressed in the future to achieve high-resolution maps of structural connectivity. From the resulting tremendous amount of data that is going to be accumulated soon, we discuss what new challenges must be tackled in terms of methods for advanced network analysis and visualization, as well data organization and distribution. This new framework is well suited to investigate key questions on brain complexity and we try to foresee what fields will most benefit from these approaches.

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Section: Brain Structural Network Analysismentioning

confidence: 99%

MR connectomics: Principles and challenges

Hagmann

Cammoun

Gigandet

et al. 2010

Journal of Neuroscience Methods

256

207

View full text Add to dashboard Cite

show abstract

“…(Christley et al, 2005;Robinson and Christley, 2007) Clustering coefficient The amount of interrelationship that exist between all the nodes and one specific node indicated complicated partnership trade patterns because it implied that when two business partners sent animals to a third location they were also linked by an animal movement (Watts and Strogatz, 1998) Shortest path length diameter…”

Section: Network Analysismentioning

confidence: 99%

“…The shortest path length or geodesic distance is the smallest number of links represented by animal movement sets required to travel from holding A to holding B (Watts and Strogatz, 1998) The diameter is the longest geodesic distance (Borgatti and Everett, 1997) Distance measurements of two-mode networks with links between rounds and holdings, must be divided by two to be compared to one-mode measurements Low values suggest that epidemic would spread quickly across the network Assortativity Preference of nodes to attach to others that are similar degree (Newman, 2002) Negative assortativity is dissortativity; high-degree nodes tend to attach to low-degree nodes Community Subset of nodes in which there are significantly more links than expected by chance; group of preferentially linked holdings (Newman, 2006) Betweenness Proportion of geodesic distances (represented by animal movement sets) between all pairs of holdings (excluding node A) that pass through node A (Freeman, 1978(Freeman, /1979 …”

Section: Network Analysismentioning

confidence: 99%

Structural vulnerability of the French swine industry trade network to the spread of infectious diseases

Rautureau

Dufour

Durand

2012

Animal

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The networks generated by live animal movements are the principal vector for the propagation of infectious agents between farms, and their topology strongly affects how fast a disease may spread. The structural characteristics of networks may thus provide indicators of network vulnerability to the spread of infectious disease. This study applied social network analysis methods to describe the French swine trade network. Initial analysis involved calculating several parameters to characterize networks and then identifying high-risk subgroups of holdings for different time scales. Holding-specific centrality measurements (‘degree’, ‘betweenness’ and ‘ingoing infection chain’), which summarize the place and the role of holdings in the network, were compared according to the production type. In addition, network components and communities, areas where connectedness is particularly high and could influence the speed and the extent of a disease, were identified and analysed. Dealer holdings stood out because of their high centrality values suggesting that these holdings may control the flow of animals in part of the network. Herds with growing units had higher values for degree and betweenness centrality, representing central positions for both spreading and receiving disease, whereas herds with finishing units had higher values for in-degree and ingoing infection chain centrality values and appeared more vulnerable with many contacts through live animal movements and thus at potentially higher risk for introduction of contagious diseases. This reflects the dynamics of the swine trade with downward movements along the production chain. But, the significant heterogeneity of farms with several production units did not reveal any particular type of production for targeting disease surveillance or control. Besides, no giant strong connected component was observed, the network being rather organized according to communities of small or medium size (<20% of network size). Because of this fragmentation, the swine trade network appeared less structurally vulnerable than ruminant trade networks. This fragmentation is explained by the hierarchical structure, which thus limits the structural vulnerability of the global trade network. However, inside communities, the hierarchical structure of the swine production system would favour the spread of an infectious agent (especially if introduced in breeding herds).

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“…The former means that networks tend to have high clustering coefficients [Footnote 1] while keeping low path lengths (Watts and Strogatz, 1998), and the latter implies that link distribution is frequently characterized by a power law, enabling highly connected nodes to appear relatively often. These two characteristics confer interesting properties to networks, like fast transmission and failure tolerance (Motter et al, 2002;Ferrer i Cancho et al, 2005;Steyvers and Tenenbaum, 2005).…”

Section: Semantic Graphs and Complex Networkmentioning

confidence: 99%

Detecting order–disorder transitions in discourse: Implications for schizophrenia

Cabana¹,

Valle-Lisboa²,

Elvevåg³

et al. 2011

Schizophrenia Research

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Several psychiatric and neurological conditions affect the semantic organization and content of a patient's speech. Specifically, the discourse of patients with schizophrenia is frequently characterized as lacking coherence. The evaluation of disturbances in discourse is often used in diagnosis and in assessing treatment efficacy, and is an important factor in prognosis.Measuring these deviations, such as "loss of meaning" and incoherence, is difficult and requires substantial human effort. Computational procedures can be employed to characterize the nature of the anomalies in discourse. We present a set of new tools derived from network theory and information science that may assist in empirical and clinical studies of communication patterns in patients, and provide the foundation for future automatic procedures. First we review information science and complex network approaches to measuring semantic coherence, and then we introduce a representation of discourse that allows for the computation of measures of disorganization. Finally we apply these tools to speech transcriptions from patients and a healthy participant, illustrating the implications and potential of this novel framework.

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Collective dynamics of 'small-world' networks

Cited by 5,935 publications

References 0 publications

MR connectomics: Principles and challenges

MR connectomics: Principles and challenges

Structural vulnerability of the French swine industry trade network to the spread of infectious diseases

Detecting order–disorder transitions in discourse: Implications for schizophrenia

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