#network science

science of networks

Grand Paris complete graph generation zoomed in_ exercise: network generation based on proximity links - first 10 iterations; territorial coverage: Greater Paris territory - smaller city area. Software: Grasshopper - Rhinoceros

To knock out the super-spreaders, the ideal target for a vaccine would be someone with many contacts in different settings—someone with a big, multigenerational family, a job that led to a lot of mixing with strangers, and a busy social life. But how do we find these highly connected individuals across 50 states and 330 million people? This is where most public health officials get stuck. To understand where the potential super-spreaders are in the general population, you would need a map of everyone's friends, family, and casual contacts—the people they see every day and those they interact with for only a few minutes. But that map, of course, doesn't exist, unless it's hiding on Mark Zuckerberg's laptop. In any case, it's not available to the Centers for Disease Control and Prevention. At this point, we need to call in a different group of experts: the physicists.

IN RECENT MONTHS, Albert-László Barabási has tried to walk around Budapest while taking calls, “to get some steps.” At 53, he is still youthful and fit, though the pandemic has kept him unusually busy. His standard route around town takes him by the peach-colored facade of the Alfréd Rényi Institute, named for a Hungarian mathematician who, with his collaborator Paul Erdős, helped lay the cornerstone of network science in the 1950s and '60s. Today the discipline informs all sorts of pursuits, from generating algorithmic recommendations on Facebook to mapping terrorist networks to, yes, forecasting the spread of lethal diseases. But when Rényi got started, he wanted the answer to a simple question: What would a network organized completely at random look like? How would it behave?

Although Erdős and Rényi were theoreticians, they thought their work might eventually have some practical application—say, in understanding the evolution of railways or the power grid. But a few decades later, Barabási and Réka Albert, his colleague in the physics department at Notre Dame, determined that the Erdős-Rényi model was actually too random to accurately describe most naturally occurring networks.

“Our first key discovery,” Barabási says, “was that there's really no random network out there.” They found that in most settings, from Hollywood to academia to the World Wide Web, networks tended to be “extremely heterogeneous, in the sense that their connectivity is dominated by a few very, very highly connected hubs.” Barabási and Albert called these networks “scale-free”: Most nodes could contact just a handful of others, but a small fraction were off the scale in terms of connectivity. Your website might link to four pages. Google links to 800 million.

“As the Fourth of July approaches, many in America will celebrate 241 years since the founders of the United States of America signed the Declaration of Independence, their very own disruptive, revolutionary startup. Prior to independence, colonists would celebrate the birth of the king. However, after the Revolutionary War broke out in April of 1775, some colonists began holding mock funerals of King George III. Additionally, bonfires, celebratory cannon and musket fire and parades were common, along with public readings of the Declaration of Independence. There was also rum.

Today, we often celebrate with BBQ, fireworks and a host of other festivities. As an aspiring data nerd and a sociologist, I thought I would use the Wolfram Language to explore the Declaration of Independence using some basic natural language processing.

Using metadata, I’ll also explore a political network of colonists with particular attention paid to Paul Revere, using built-in Wolfram Language functions and network science to uncover some hidden truths about colonial Boston and its key players leading up to the signing of the Declaration of Independence.”

TL;DR