Robustness of a network

The following graph is the final network model state as discussed in my previous blog (http://businessfractal.blogspot.com/2013/08/to-rent-or-buy-dashboard-analytical.html), where I indicated the ability to determine the robustness of a network from a network simulation (http://youtu.be/oBb5RjorMP8).

 

The key statistics of the network can be found as being:

Number of Vertices: 303

Number of Edges: 326

Diameter of network: 13

Mean Degree of the network: 2.151815

Maximum Degree of the network: 32

Mean Geodesic of the network: 5.136059

Density of the network : 0.0071017

Transitivity of the network:0.003640777



Robustness of the network can be tested in two ways, first by attacking the highest connected hubs in a structured manner, and then by removing nodes in a random manner. The simplest measure to test this impact is the average distance (mean geodesic) of the network. The following graphs shows a few simulations by removing 55% of nodes in the network. The blue line shows the failure in the average path if a structured attack is carried out, with the red lines resulting from random attacks. From a structured perspective this network is highly fragile, failing in less than 1% of node removals, where-as the network is quite robust when being attack in a random manner. Whether this is good or bad naturally depends on the application; if we want to design a marketing campaign, then we might rather use a structured approach to implement it, as apposed to a random approach. If it is a supply chain network, the structured attack will be of high concern from a risk management perspective.

 
Finally, analysis of the network model indicates that this model is a scale-free network, as the connection degree do follow a power-law behaviour, which does indicates the reason for the network fragility under structured and random attacks.