Untraceable: The Disappearing Node
This past Friday I had a guest lecturer in my discrete math class that lectured on how to isolate connected components from a large networks data set of nodes and edges, such as Facebook. This lecture, other than being suprisingly relevant and convenient for my blog, brought up the idea that we can judge a connected component exists when we are unable to tell where in the cluster of nodes a meme originated (for the sake of this commentary, a meme will be defined as any form of idea or thought). A meme propagates at a high rate within a connected component because those in the connected component have a strong tie to each other so they are much more likely to spread the meme amongst themselves before spreading it outside their component. The lecturer proposed that at the point when the meme is so widespread within a component that you can’t find the source and it has yet to spread past that component than the nodes in that section are connected components. This idea was initially difficult to grasp for me but when I began putting it in context it both made perfect sense and led me to make another conclusion about networks.
Putting the idea in the context of the real world showed me that all groups of friends really do operate the way the idea proposes. One way to show this was to look at inside joke. Have you ever had a really funny joke that you told a friend and maybe a week later he tells that same joke back to you? I know its happened often to me. When you hear a joke or see a funny video on youtube who do you tell first? Your closest friends! Well of course your closest friends will tell their closest friends. And as this joke or video is spread there comes a point where those you have shared the meme with forget who originally thought up the meme. It is at this point when you can look at those that know the meme and determine that they are in your connected component. Of course there is a possibility that one of your friends spread your meme outside your group of friends before the proposed time, but the probability of this occuring in a group of tightly connected friends is extremely small as anyone outside the connected component has few edges into the connected component, and from class we know that these nodes are also weak ties which lowers the odds even more. From the inability to remember the source of the meme in even a small connected component, I came to a suprisingly obvious conclusion that it is amazingly easy to disappear in a network.
Although it took me two paragraphs to get here, (I wanted to show how convoluted the steps to this conclusion were and since they were still relevant I included them) I will finally talk about the news article I linked to this blog. This news article relates to the conclusion I came to, that it is easy to disappear in a network. First let me elaborate, when I say disappear I mean that it is impossible to trace you based on your connections in the network, In networks, and often outside class, we are told that if we take six steps along our network we are connected to pretty much anyone on the planet. Well my conclusion simply takes that and says if you go six steps from someone and forget those six steps you have virtually no way of finding that person again using your network. As an example of how this conclusion plays out in real life, I give you the “fast and furious operation” discussed in the article. The operation involved selling tagged weapons to known or suspected buyers for Mexican cartels and tracking these weapons to bust the leaders of these cartels. Now this might have succeeded had we actually been able to track every individual weapon, but on occasion surveillance was slackened and the weapons changed hands. Now this is where my conclusion comes into play. The minute the weapon had taken an unknown path (edge) from the known location (node) the number of locations it could be rise enormously. Now it might be okay if you can cover this mistake and find the one location its at now using all your resources, but if it changes hands again the exponential rise in possible locations will just be too much to handle. After that it will only change hands again and again and, as the operation found out, your weapons can be anywhere now.