NetSci in 1 minute
During the study of many different disciplines, scientists have come across a diverse set of complex systems that are organized in a networked fashion. Some examples include computers interconnected to form the Internet, social networks of friendships and acquaintances, academic networks of co-authorship and collaboration, utility networks of the energy grid, transportation networks of cities and roads. The list goes on. What all of these systems have in common is that they are all formed by a set of interconnected entities, to form a distributed, scattered system that is, in many cases, more than just the sum of its parts.
Network Science arises from the effort to gather up all research about networks under the same regime. In its most basic form, it eliminates the identity of the networks, and focuses on the organizational structure only, also known as the network's topology, through the study of mathematical objects known as graphs. In its applied form, it deals directly with the networks themselves, manipulating massive amounts of real-world data, with applications to Computer Science, Sociology, Physics, Economics, and Neuroscience.
NetSci in 10 minutes
What does Erdos mean, anyway?
During the mid twentieth century, Hungarian mathematician Paul Erdos became known for his passion for mathematics, his eccentric demeanor, and his astoundingly prolific output. He published more than 1500 articles in many different areas of mathematics, including graph theory, the mathematical toolbox underlying Network Science.
Erdos had around 500 direct collaborators for his publications, and due to his fame and the prestige it meant to publish with him, his colleagues invented the notion of an Erdos number. Erdos himself got an Erdos number of \(0\), while his direct collaborators were assigned the number \(1\). Collaborators of Erdos' direct co-authors received an Erdos number of at most \(2\), and so every person is assigned the smallest value among all their collaborators plus one.
The Erdos number also defines an interesting social network of scientific co-authorship, in which we can identify authors as the entities, or nodes, of the network, and we can mark the existing co-authorships as relationships, or edges, in the network.
You can see how this network looks like here.
In this way, Erdos was not only an expert in graph theory, but he also wove a real interconnected network of mathematicians, scientists and authors. The Erdos number is part of the folklore of mathematics and academia, used to this day as a tongue-in-cheek ranking among the academic community. There is even a Bacon number, defined much in the same way but around actor Kevin Bacon, which traces the network of collaboration among stage artists.
It is a small world, after all
Around the same time, in the 1960's, Stanley Milgram conducted several experiments known now as the small-world experiments. He chose people at random in Omaha, Nebraska, and asked them to forward a letter to a certain person in Boston, Massachusetts. If the chosen person didn't know the recipient in Boston, they were to forward the letter to an acquaintance of their choosing, given that the next person person to receive the letter had a higher chance of knowing the original recipient.
Milgram then tracked the correspondence chain and studied the number of steps that it usually took a letter to reach the intended recipient. To his surprise, the average number of steps was between five and six. This and other results are now widely known as the rule of six degrees of separation, and it has led researchers to further investigate the properties of large social networks.
One would expect that Milgram's letters would have arrived after dozens of steps, since they had to cross more than 1,000 miles and had to be routed through millions of people. As it turns out, many real-life networks exhibit the same pattern where any two nodes are likely to be connected by a surprisingly low number of steps. This is a measured called average path length. When a network has low average path length relative to the number of nodes, scientists say it's a small-world network.
Since then, evidence have been found that supports the fact that many other networks are also small-world: from real-life and online social networks to cities interconnected by a network of roads, networks of protein interactions, and even networks of brain cells.
NetSci in a little more than 10 minutes
If you're ready to spend some more time learning about Network Science, you can start with our challenges or resources pages.