In most networks, there are elements that have a huge amount of direct connections to others, and these individuals tend to be rather important. They are called super-spreaders or hubs.
A complete overview of interbank exchanges would help prevent a new financial collapse. However, banks do not provide this information: this is why a “network reconstruction” methodology to infer the unobserved connections is needed.
During the Corona pandemic the reproduction number appeared in much of the media. While it is not at all obvious what this quantity measures exactly, it is obvious that making it smaller than 1 really is crucial in controlling the spread of the virus. So what is this really?
In 2016 a company calculated that the average number of followers in Twitter was about 707. Although this might already sound like a lot, it pales in comparison with the top Twitter users. There are currently more than 100 users that have more than ten million followers. Some, like Barack Obama or Katy Perry, even have more than one hundred million followers, which is roughly 140.000 times larger than the average.
Many networks, from technological to social networks, and from the world-wide web to collaboration networks, have a hub-like structure. Why is this the case, and why are they not much more homogeneous?
The moment millions of fans have waited for is there: the finale of Game of Thrones. 75 characters in different parts of the world, fighting to be the ruler of the iron throne. But who is the mathematical ruler of the iron throne?