Proc Natl Acad Sci USA. Some features of the spread of epidemics and information on a random graph

[Giuseppe]

Some features of the spread of epidemics and information on a random graph (Proc Natl Acad Sci USA, abstract, edited)

[Source: Proceedings of the National Academy of Sciences of the United States of America (PNAS), OpenAccess Abstract and PDF Article: LINK. EDITED.]

Published online before print February 18, 2010, doi: 10.1073/pnas.0914402107
PNAS March 9, 2010 vol. 107 no. 10 4491-4498

Free via Open Access: OA

Some features of the spread of epidemics and information on a random graph

Rick Durrett,1 - Department of Math, Cornell University, Ithaca NY 14853


This article is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2007.

Edited* by Simon A. Levin, Princeton University, Princeton, NJ, and accepted by the Editorial Board January 4, 2010 (received for review December 14, 2009)


Random graphs are useful models of social and technological networks. To date, most of the research in this area has concerned geometric properties of the graphs. Here we focus on processes taking place on the network. In particular we are interested in how their behavior on networks differs from that in homogeneously mixing populations or on regular lattices of the type commonly used in ecological models.

complex networks ∣ power-law degree distributions ∣ contact process ∣ random Boolean network ∣ voter model

Author contributions: R.T.D. wrote the paper.
The author declares no conflict of interest.
*This Direct Submission article had a prearranged editor.
Freely available online through the PNAS open access option.
1To whom correspondence may be addressed. E-mail: rtd1@cornell.edu.

-
------

 

[Sally Furniss]

Re: Proc Natl Acad Sci USA. Some features of the spread of epidemics and information on a random graph

Access to free article (PDF) here

 

[gsgs]

Re: Proc Natl Acad Sci USA. Some features of the spread of epidemics and information on a random graph

isn't it allowed to link directly ?
http://www.pnas.org/content/early/2010/02/17/0914402107.full.pdf

who writes a summary ?
not so easy to see the relevance for epidemics (if any)

> ...,which is biased...

 

[Sally Furniss]

Re: Proc Natl Acad Sci USA. Some features of the spread of epidemics and information on a random graph

Thank you gs. I was having problems with that link yesterday which is why I put in the other one.

 

[gsgs]

Re: Proc Natl Acad Sci USA. Some features of the spread of epidemics and information on a random graph

a (undirected,finite) graph has n vertices and a n*n binary matrix to show
which vertices are connected to which others.
"graph-theory" examines the properties of these graphs, showing
existence,non-existence,classification of graphs with certain properties.

For many vertices (populations) of ~1M the matrix is too big
to store and examine.
But when each vertex is only connected to a few (<1000) others,
("small world")
then you needn't store the whole matrix, just the list of "neighbors"
for each vertex.

These lists can then be used in computer-simulations to examine
network behaviour, telefone-networks, social "clubs", epidemics,...

average number of common friends
speed of message-spread , infectious disease spread
change of voting behaviour
size of connected components
lengths of average shortest path from one member to another