A super-connected backbone (shown in red) appears as more links are added to a network. (Image: Raissa D'Souza/UC Davis)

US computer scientists have found that random networks – the mathematical description for networks we experience everyday in forms such as the internet and global flight connections – have the potential for extreme behaviour never seen before.

Their findings might lead to improved understanding of how to control such networks – for example, to halt the spread of epidemics or improve the efficiency of delivery networks.

The researchers, led by Dimitris Achlioptas at the University of California at Santa Cruz, have been playing a Buckaroo-style game, adding more and more connections between points, or nodes, in a network to see what happens.


Networks that grow randomly, like the global connections between computers that make up the internet, usually rapidly and smoothly gain a central backbone of connections that make it simple to travel between any two points, in what is called a fully connected structure.

Explosive change

The team has used simulations to find a way to grow a network randomly, but significantly delay the emergence of that backbone. But rather like the mule in Buckaroo, when the network does become fully connected it is with an explosive kick rather than a gradual change.

Random networks are usually grown by selecting two nodes at random to become connected. Instead, Achlioptas’ team pick two pairs of random nodes, but only connect one of them – the pair with the fewest pre-existing connections to other nodes. That’s rather like giving a Buckaroo player two choices for where to place the next item on the mule’s back and allowing them to pick the spot that is least likely to cause the mule to kick.

The result is that for a long time the network grows, but does not become fully connected. Instead it contains a large number of unconnected chunks, each containing a few nodes. Eventually, the addition of just one link triggers an instantaneous phase change and the network becomes fully connected.

Achlioptas’ team call the transition “explosive percolation”. A variation on this technique makes it possible to carry out the opposite process and accelerate the arrival of a network’s backbone.

Virus control

The “million dollar question” is whether, or how, the new discovery affects real-world networks, says Raissa D’Souza at the University of California, Davis, a member of the research team.

“We know that for some networks, like the internet, connectivity is a fundamental desired property” she says. “For others, like a virus spreading through a network of humans or computers, connectivity is a liability.” So, for example, delaying connectivity could have an impact on preventing viruses becoming endemic in a human population via the random networks that are people’s social links.

Journal reference: Science (DOI: 10.1126/science.1167782)