Modelling AIDS-Epidemics or any venereal disease on random graphs

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

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Afterword

10.1093/oso/9780198789789.003.0008 ◽

2017 ◽

Author(s):

Katherine Paugh

Keyword(s):

Infant Mortality ◽

African Descent ◽

Venereal Disease ◽

British Caribbean ◽

Nineteenth And Twentieth Centuries ◽

The Caribbean ◽

Late Nineteenth

The strategies for the management of reproduction in colonial settings that emerged during the age of abolition continued to reverberate in the British Caribbean in the mid to late nineteenth and twentieth centuries. The supervision of midwives of African descent by British and white creole women, concerns about supposedly racially characteristic venereal disease, and a tendency to blame infant mortality on the sexual and parental irresponsibility of laborers, all continued to characterize governmental supervision of colonial reproduction in the Caribbean.

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Random graphs

10.1093/oso/9780198805090.003.0011 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Random Graph ◽

Random Graphs ◽

Large Scale ◽

Random Network ◽

Graph Model ◽

Clustering Coefficient ◽

Giant Component ◽

Random Graph Model ◽

Definition Of ◽

Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

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