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I'm a math major with a current interest towards network theory. A network can be considered as a collection of nodes, and edges between these nodes signifying some relation between them. The most ubiquitous example would be a social network like Facebook with nodes representing people, and an edge connecting two nodes if they're friends.

A network is called directed if the edges have a direction. This means that if there's an edge directed from A to B, it's not the same as an edge from B to A. An example of this would be a food web network, where the nodes represent species and an edge from species A to B means that A eats B. Obviously, this does not necessarily mean that there's an edge from B to A (rarely does the prey eat the predator).

A network is called undirected if it is not directed, i.e. none of the edges have any direction; if there's an edge from A to B, it necessarily means that there's an edge from B to A.

Now, one can assign weights (numerical values) to the edges in a network to signify the relative importance of edges. In the Facebook example above, this can be considered akin to assigning values to edges which indicate the strength of friendship/distance between the residences of friends, etc.

I wish to study ecological networks to see if I can make interesting inferences from my study of weighted networks.

So can you give me some examples of undirected, weighted ecological networks?

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    $\begingroup$ Network theory finds wide application in trophic ecology (food webs) and genetics (gene regulatory networks). Have a look at that. $\endgroup$ – Hav0k Oct 30 '15 at 8:25
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    $\begingroup$ Interaction/foodweb networks where we only know the correlations between species (e.g. correlations between the abundances of species over time) would be one example of a undirected, weighted network. $\endgroup$ – fileunderwater Oct 30 '15 at 8:45
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Epidemiology, the spreading of diseases, is probably one of the most famous applications of network theory in biology, going all the way back to John Snow.

A more relevant example would maybe be something like graph models of habitat mosaics. Populations are often both spread out over landscapes and clumped together in smaller pockets of suitable habitats. While fragmented, these populations still have a certain amount of contact, resulting in gene flow and the creation of what is often called a meta-population. These things can happen on a vast range of scales, from your back yard to whole continents, but by modeling them like graphs they can all be studied comparatively and tested for resilience agains disturbances, habitat loss etc.

You mention social networks, but there is no reason why you can't study the same in animal populations. Say one individual learns something useful, maybe the location and route to a rich feeding ground. That information can then be shared with other individuals, either by show-and-tell, or maybe by some kind of abstract communication. The information spreads in familiar exponential fashion until everyone knows, then any one of those individuals can relay or be "eaves dropped" on by a neighbouring population, it doesn't even have to be the same species in some cases, and the information flows again. As with the habitat mosaics the benefit of these models is that very different systems can be compared and tested on an equal footing, anything from fish, to birds, mammals, even some social insects, lend themselves well to this.

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  • $\begingroup$ Started working on an answer, then decided just to upvote this one. Some undirected, weighted networks for epidemiology can be found at ndssl.vbi.vt.edu/synthetic-data , or as component of the ergm R package, if one is so inclined. $\endgroup$ – Fomite Jan 29 '16 at 20:07

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