Network Tolerance Page

Summary

We are interested in studying the robustness of network with respect to its function and structure. Specifically, we would like to investigate the effect of perturbations of network structure on its function and dynamics.

Deliverables

Members

Jessica Santana jsant@stanford.edu
Junjian Qi
Claire (lagesse.claire at gmail.com)
Alireza (alireza.goudarzi at gmail.com)
Ali Kharrazi

Meetings

(1) [DONE]Friday, June 13, 2014 - Agenda: Define the topic -- We will study the robustness of dynamics/function of network with respect to changes or perturbations in the structure of the network. - Goal for next meeting: -- Each group member look for interesting example of robustness in their field and discuss it.

(2) Monday, June 16, 2014 - Agenda: Discussion of examples of robustness in different disciplines. - Goal: define the scope of the project and decide on the model.

Ideas: Working draft

Claire: Failure Tolerance in Networks - What about the road network ?

Let's picture a road network where nodes are roads and edges the intersections between roads. We can apply to each node a weight, given (for instance) to the length of the road it is representing. Thus, to go from one node to the other, there is a shortest path, witch minimize the number of nodes crossed. We can adjust this shortest path for it to take into account the weight of the node. So maybe it will readjust itself, crossing more nodes but with a minimal weight. If we want to consider the local tolerance of the network, we can increase gradually the weight of one node (randomly chosen - or not), as if the energy needed to cross this node is gradually more and more important. Then we can quantify the point where the shortest path is readjusting itself to prefer another node from the first one. This could quantify the tolerance of this node on the network. On a more global approach, if we calculate all the shortest paths of the network it will give us the betweeness of each node. We can see how this betweeness is readjusting on the whole network when the weight of a central node is increasing. It would be interesting to point the critical values for a given network. In this way, it would be possible to characterize the tolerance of a network to an increase weight perturbation on nodes given on its topology.