How math can help us understand terrorist networks

Science Friday
A general view of the site of a suicide car bomb attack

A general view of the site after a suicide car bomb attack at the shopping area of Karrada, a largely Shiite district, in Baghdad, Iraq, July 4, 2016.

Ahmed Saad/Reuter

Extremist groups like ISIS have utilized social media platforms to extend their global reach and message. Even with companies suspending accounts affiliated with these groups — for example, since mid-2015 Twitter has closed 125,000 — extremist groups can still be found on various social media platforms.

In two studies, published in Science and Science Advances, a group led by physicist Neil Johnson tracked the growth and decline of extremist networks on social media platforms through mathematical models typically used to map complex systems in the natural world. 

Johnson began his research by studying terrorist networks on the Russian social network, VKontakte. He says the behavior of people online can be mathematically compared to the movements of marine life or galaxies. 

“It’s very interesting,” Johnson says. “Just like in marine ecology ... fish form into groups, and they form into bigger groups, and they fragment when any predator or any sense of danger is around. There are moderators on VKontakte, there are actual hacking groups out there trying to target ISIS, it’s almost like a natural ecology. And this is the key thing that, whereas agencies tend to take a very individual approach — I mean who is the leader, who is the person who's sending the orders — what we found is it's very much like an ecology. There is no one object driving the ecology. It is a collection of objects that together build the threat. And it's by understanding that, that we believe holds the key to moving forward.”

Johnson’s study has led to new ideas about how to break apart dangerous extremist groups. The key, he thinks is using viral internet strategies to spread counter-terror ideas. 

“One way we've been looking at is very much like one would look at, say, the spread of a meme, the spread of an idea,” Johnson says. “Once you have the mathematical model — which we have now of how the groups develop, the timescale at which they develop, how quickly, when they break up — we can detect, we can actually see what would need to be introduced into a group so that it would spread like a meme. ... What would it take to get that counter idea spreading quickly to all of these different component groups?” 

Johnson also thinks his mathematical models might be able to predict when an online group might develop into something more dangerous. 

“If we take a snapshot just today of our data, there are a number of individuals online that do not look like they're connected to these groups, but they have been in the past," he says. "That trajectory of where they have come from carries then the information that what might be going on in their mind, and ... what therefore looms on the horizon for them, and therefore what they might be, what they might have intent and capability to actually do.”

Johnson’s work has also uncovered unexpected findings about the role of women in online terrorist networks. 

“Definitely a majority are men, but the women, when you look at the network of users, the women are like the glue that holds this network together,” Johnson says. “The position of the women users we found was a very clever one. It had a particular property called betweenist centrality ... which is ... being the glue of the network rather than the visible face of the network.”

The modeling is still being developed, but Johnson says the potential to predict terrorist activity is there. 

“It's very much like, for example, if I go to heart doctor. I don't expect that doctor to tell me ... I definitely would have this happen on next Thursday, or it will be definitely in three years. It's a case of raised, elevated probabilities," he says. "But these are probabilities based on hard data, and backed up by a mathematical model.”