Have you ever wanted to send a message to someone with whom you do not have direct contact? What if you knew a friend who had direct contact with this someone? You could send the message through your friend.
This principle can be modeled geometrically. Let’s say you are A and the person with whom you want to speak is C. There is no direct link between A and C.
However, your friend, B, knows this someone, C. So there are links between you, A, and your friend, B, as well as your friend, B, and this someone, C.
Thus, your friend, B, can serve as a bridge, linking you and this someone, and a triangle is formed.
Although when presented geometrically this process may appear abstract, we are familiar with the practice in everyday settings. For instance, we link two contacts via an introduction email, or we introduce two friends at a cocktail party. Triangles are a divine geometry, as they serve to create new connections.
With the US Political season on the horizon, let’s use Twitter and apply this geometry to Republican Presidential Candidate Donald Trump, @realdonaldtrump. Trump follows 44 twitter profiles, one of which is that of Bill O’reilly, @oreillyfactor. O’reilly follows 37 twitter profiles, one of which is that of Donald Trump. So there is a two way connection between Donald Trump and Bill O’reilly.
Well Let’s image this two way connection did not exist and that Donald Trump wanted to connect with Bill O’reilly. How might the two connect? Yes, we must find the common links between Trump and O’reilly, that is the twitter profiles that they both follow. When conducting the analysis, via Python, we find that there are 4 twitter profiles that both Trump and O’reilly follow. The four profiles are @foxandfriends, @BretBaier, @greta, and @ericbollinger . Again, here’s the visualization from above.
To connect with O’reilly, Trump could form a triangle from any of the four. The more links, the greater the likelihood a connection will be made. Triangles create opportunities for our message to reach peripheral networks, without us having to directly transmit the information to the end recipient.
Therein lies the true power of social networks.