Mubarak's first major attempt to squash the revolution was turning off Egypt's internet on Jan 28. This was shortly followed by an escalation of violence, and Cairo turning into a battleground between the revolutionaries and pro-regime thugs. What happened when the internet went down, and the future of Egypt hung in the balance?
The answer seems to be that the shutoff certainly had a large impact, but it wasn't nearly enough to disrupt the overall network.
By looking at the Twitter timelines of the people in the network from my post Visualizing the New Arab Mind, we can determine which people were affected by the internet shutdown. If the person is tweeting less than half as much during the shutdown in comparison to their normal rate, we color them red. (Some nodes have been removed due to a lack of data)
We can see that the shutdown affected a huge swath of the network, yet those network regions remain dense with active nodes. No one is too far socially removed from someone who still has access to the internet.
We can also take a look at the specifics of when people were tweeting. In the below diagram, we plot every single tweet from this network from Jan 24 to Feb 3. Each node in the network now corresponds to a row of tweets, placed in time. We can see a dramatic cliff on the 28th as service is suddenly interrupted. But soon, many of the nodes are finding a way to tweet at least a little. Cutting the flow of information out of Egypt just wasn't going to happen.
Another notable pattern is the substantial surge in tweets from the people in blue during the blackout period. Clearly a large number of people were alarmed by these developments and increased their tweeting in response. Looking at what they are saying, and if/how they are relaying information from their disenfranchised friends, would be the next step in understanding how the network responded to this challenge. 
It's also worth noting that not only were some of the nodes shut off in terms of internet, but also as citizen participants. There were a large number of arrests and temporary detentions, which caused people to go offline. This is also a phenomena worth looking into. 
Experts say Egypt is the crystal ball in which the Arab world sees its future. Now that Mubarak has stepped down, I can share the work I've done making that metaphor tangible, and visualizing the pro-democracy movement in Egypt and across the Middle East. It is based on their Twitter activity, capturing the freedom of expression and association that is possible in that medium, and which is representative of a new collective consciousness taking form.
The map is arranged to place individuals near the individuals they influence, and factions near the factions they influence. The color is based on the language they tweet in -- a choice that itself can be meaningful, and clearly separates different strata of society.
Many fascinating structures can be seen. Wael Ghonim, a pivotal figure in this self-organzing system who instigated the initial protests on January 25th, is prominently located near the bottom of the network, straddling two factions as well as two languages. The size of his node reflects his influence on the entire network. 
The lump on the left is dominated by journalists, NGO and foreign policy types; it seems nearly gafted on, and goes through an intermediary buffer layer before making contact with the true Egyptian activists on the ground. However, this process of translation and aggregation is key; it is how those in Egypt are finally getting a voice in Western society, and an insurance policy against regime violence. Many of the prominent nodes in this network were at some point arrested, but their deep connectivity help ensure they were not "dissapeared".
Most of those in this network speak both English and Arabic, and their choice of language says a lot about both the movement and about Twitter. Some may choose to primarily communicate with their friends, while others make an effort to be visible to the rest of the world on purpose. They want to reach out, and connect with, the rest of the global society. The structure on the bottom, near Ghonim, seems entirely composed of this free intermingling. 
In a case of ironic symbolism, the far left-most satellites are the Whitehouse, State Department, and Wael Ghonim's employeer, Eric Schmidt, who is merely a speck on the map. And that's probably how everyone in the rest of the network would like this future to look. 
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********* UPDATE ********
@muziejus points out that I didn't elaborate much on the first paragraph. For me, the point is that the activists are cooperating with the west, on their own terms and in a constructive way. Activists are not embarrassed to be tweeting in English, in fact that is a key element and what allows this much bigger exoskeleton to tightly interface to the core. This is in contrast to what happened in Iran 2009 (see the panel "Disruptive Events Lead to Information Elites"), where the connections between those in Iran and the rest of the world were very thin and easily severed.