Lecture #17: Presentation by Anusha & Random Networks

Anusha gave her presentation on Food Webs. Food Webs are complex networks formed by on e species of animals feeding on the other species. She is exploring 16 species of which target species that when extinct can cause a large number of species of animals to go extinct or or near extinct. Food webs are more robust in case of random species removal than in case of removal of species with many links to other species. Food webs with high connectance displays high sensitivity from the beginning and loss of any species causes reduction in robustness irrespective of their connections.


Professor talked about Random Networks
G(n,m) is a random graph with n nodes and m edges. How do we generate one?
Randomly create nodes
Randomly select 2 of those nodes and connect with an edge. Repeat this step.
May end up with directed or undirected so purely random. Another way is to randomly create a node and for each node after the 1st you connect it to a random node. End up with n-1 edges and a directed graph, so not purely random.

P(G) = P^m (1-P)^((2^n)-m)
m=(n/2)P
P = m/(n/2) is the probability of having an edge. Includes self loops, but not double edges.
= (2/n)P
= 2m/n = (2(n/2)P)/n = (n-1)P
C = /n-1 goes to zero as the size of the network increases.

Random graphs lack high clustering & degree.
Key Points: Generation Model