Last time we talked about connectivity in networks.
Today we're going to talk about how connectivity relates
to the robustness of a network.
So, what is network robustness?
The way we loosely define network robustness is the ability
of a network to maintain its general structure, or
its general functions when it faces failures or attacks.
So what kind of attacks are we talking about here?
Well, we're going to talk about attacks that are in the form of removal of
nodes or edges.
This could be somebody purposely trying to remove a node or an edge from a network,
or maybe, just random failures that the network may have.
And then what are the general properties that we are going to be discussing?
In this case we're going to be talking about connectivity, so
robustness is going to be the network's ability to maintain its connectivity.
When it loses some of its nodes or some of its edges.
So why is this relevant?
Why is this important?
Let's look at some examples of networks that often lose nodes or edges.
And these things affect the function.
So one example is the air transportation network,
where the nodes are airports and the edges are connections between airports.
Well, sometimes airports have to close down for many different reasons.
And when this happens of course, transportation is affected.
And so you would like for the transportation network to be robust to
closures of airports, so that the general connectivity or the general function of
the network is still maintained even after it might have lost one particular airport.
Or maybe it's not an airport, maybe it's a connection between an airport or
some other airport.
Maybe both airports are open but they're not able to fly to each other for
whatever reason.
That is the case where the network might have lost an edge rather than a node, and
you would like for the network to still maintain its connectivity or functions.
There are plenty of other examples like Internet router failures or
power line failure and so on.
And so for all of these, this idea of removing nodes or
edges are things that actually happen, and
for all of this maintaining connectivity is very important.