Uncovering complex network structures in nature

December 09, 2014

The global spread of Ebola is due to the complex interactions between individuals, societies, and transportation and trade networks. Understanding and building appropriate statistical and mathematical models of these interactions is vital to responding to the challenges of living in a networked world. There are, of course, many other examples of complex networks -- from national power grids and airline networks to social networks, neuronal networks and protein-protein interactions.

In a new study published in the Beijing-headquartered journal National Science Review, scientists based in China and Australia state that in complex systems, to understand the behavior of the system it is becoming necessary first to properly chart the structure of the network.

In an article titled "Random complex networks," Michael Small, based at The University of Western Australia, Lvlin Hou, based at China's National University of Defense Technology, and Linjun Zhang, a PhD candidate at University of Pennsylvania, note that in physics and mathematics, one typically characterizes the structure of complex networks by looking at the connections between individual components, and creating a distribution - the node degree distribution - characterizing the expected number of connections for a random component.

In some systems, they add, individual components have a similar number of neighbors - most traffic intersections are junctions of two, three or four roads. In other systems the numbers vary wildly - some websites have only a few links pointing at them; others have many tens of thousands. Most proteins interact with only one or two others; some form thousands of interactions. Most people have a few friends (or colleagues, or contacts); some have many more. Systems exhibiting this wildly varying degree of connectivity are an extreme challenge for mathematicians and physicists to describe: what does one mean by choosing one of these systems at random? How should those connections be configured?

Co-authors of the paper "Random Complex networks" seek to answer these questions.

Several models have already been proposed to generate networks of interacting individuals with wildly varying connectivity. The most famous of these is known as preferential attachment and follows the social maxim of "the rich get richer". As time progresses, the individuals in the network with the most connections are the ones most likely to acquire new connections. Just as in the real world, wealth attracts still more wealth and societies develop with most people having little and a small minority having most of the resources.

While this is intuitive, it turns out that there is a much richer and more interesting structure of complex networks that is not explored with this approach. Co-authors of the National Science Review paper provide a solution by proposing a simple method to fully explore the mathematical space of all "interesting" networks with a particular node degree distribution. They achieve this aim by randomly exchanging edges on the network.

This simple process (justified with some less simple mathematics) allows scientists to explore the behavior of typical networks. This process can be applied to experimentally obtained networks (from airline transportation networks, to gene interaction, Internet, social connections and so on) to probe which features of the individual networks are the really important defining structures.

While the preferential attachment model is a common approach to construct such networks, the co-authors of the new study show for the first time that features of this model are not typical. In particular, preferential attachment networks are "robust-yet-fragile". That is, by random deleting parts of the network, the overall network structure is largely unaffected (the robustness part). However, deliberately attacking particular nodes in the network can quickly lead to complete collapse (fragility).

It was thought that this is a common property of all networks with such wildly divergent degrees of connection. However, there is mounting evidence that many systems do not have this property. The new study shows that most typical networks are robust to both random and deliberate attacks. This result provides a better explanation of earlier observations of many natural and technological complex systems.
See the article:

Michael Small, Lvlin Hou, and Linjun Zhang

Random complex networks

National Science Review, 2014, 1(3): 357-367


The National Science Review is the first comprehensive scholarly journal released in English in China that is aimed at linking the country's rapidly advancing community of scientists with the global frontiers of science and technology. The journal also aims to shine a worldwide spotlight on scientific research advances across China.

Science China Press

Related Social Networks Articles from Brightsurf:

AI methods of analyzing social networks find new cell types in tissue
In situ sequencing enables gene activity inside body tissues to be depicted in microscope images.

Teen social networks linked to adult depression
Teens who have a larger number of friends may be less likely to suffer from depression later in life, especially women, a new MSU research study has found.

Drexel study: Measuring social networks of young adults with autism
While social isolation is a core challenge associated with autism, researchers from Drexel University's A.J.

Study suggests optimal social networks of no more than 150 people
New rules of engagement on the battlefield will require a deep understanding of networks and how they operate according to new Army research.

Social networks can support academic success
Social networks have been found to influence academic performance: students tend to perform better with high-performers among their friends, as some people are capable of inspiring others to try harder, according to Sofia Dokuka, Dilara Valeyeva and Maria Yudkevich of the HSE University.

Brain builds and uses maps of social networks, physical space, in the same way
Even in these social-distanced days, we keep in our heads a map of our relationships with other people: family, friends, coworkers and how they relate to each other.

Twitter fight: Birds use social networks to pick opponents wisely
In a new article published in the journal Current Opinion in Psychology, UC biologist Elizabeth Hobson says animals such as monk parakeets seem to understand where they fit in a dominance hierarchy and pick their fights accordingly.

Study questions benefits of social networks to disaster response
Faced with a common peril, people delay making decisions that might save lives, fail to alert each other to danger and spread misinformation.

'McDonaldization' based analysis of Russian social networks
The author describes his concept this way: 'the principles of the fast-food restaurant are coming to dominate more and more sectors of recent'.

Hunter-gatherers facilitated a cultural revolution through small social networks
Hunter-gatherer ancestors, from around 300,000 years ago, facilitated a cultural revolution by developing ideas in small social networks, and regularly drawing on knowledge from neighbouring camps, suggests a new study by UCL and University of Zurich.

Read More: Social Networks News and Social Networks Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.