It may be difficult to see what power grids, flight schedules and immunization strategies have in common, but all are examples of the networks a group of Boston University researchers are studying to try and find patterns.
College of Arts and Sciences physics professor Eugene Stanley, who is directing the research, said all networks are connected in certain patterns, regardless of whether they are social relationships, the spread of diseases or the interstate highway system. These “scale-free,” networks, which have varying numbers of branches, are centered on a few large hubs, called nodes, in the same way flight patterns center around a few large cities.
The hubs led to the discovery of one commonly known pattern in human social relationships – the theory of “six degrees of separation,” which states every person on earth can be connected through six social relationships.
“The question is how to describe these networks,” Stanley said. “We do this by finding a regular feature, a concrete equation that can be applied to lots of different things.”
Understanding networks enables people to use them more efficiently. For example, knowledge of networks has been used to create a more effective immunization strategy.
“Stopping the spread of a contagious disease is creating a break in a network,” said Sameet Sreenivasan, a College of Arts and Sciences graduate student who worked on the project. “In order to minimize costs, you want to remove or immunize the minimum possible number of nodes.”
Because people have varying numbers of social interactions, a strategy called acquaintance immunization is more effective than random immunization. Now, instead of immunizing themselves, people can give the name of an acquaintance that needs to be immunized. Because he or she would know so many people, the “hub people,” those with lots of friends, will be immunized and will stop the spread of a disease.
Toshi Tanizawa, a university researcher, said he works to protect networks from such attacks. He has found that the networks in which most nodes have few links and some nodes have many links are the most robust against both targeted and random attacks.
This can be used practically for power grids, which are susceptible to both small random failures, such as downed lines in inclement weather, and larger targeted attacks from outside agents, such as terrorists.
“We figured this out not through simulation, but by analyzing actual data,” Tanizawa said. “This makes our results much more reliable.”
The next step in Tanizawa’s research involves the repeated removal of nodes through various types of attacks.
CAS graduate student Eduardo Lopez said he looks at how the shapes of networks affect how things move within them. He said he has found that the rate of transmission is dependent on the number of neighbors a given node has, but not necessarily where the nodes are in relation to each other.
“It is useful for knowing, for example, how much input you need at one end of the power grid to keep electricity flowing to every house in the system,” Lopez said.
Zhenhua Wu, a CAS graduate student, also deals with movement within a network. He related his discovery about optimal routes for driving.
“Say you want to get from your office at BU to the airport,” he said. “You don’t necessarily want the shortest route, you want the route that takes the least time even if that means going further.”