Getting too Big
From a conversation with a friend of mine about the role of hubs in scale-free networks we were intrigued if too large hubs were indeed good for a network since they control and process most of the information flowing through the network. This is particularly alarming in the context of economic networks. Contemporary economic globalization is leading us to a star-topology (1) pattern in our leading economic networks. The hubs of global economy are growing as each new major merger reaches the news. The major hubs are distancing themselves from the following nodes at an ever increasing rhythm. Economist pioneer Vilfedo Paretoâ??s 80/20 Rule is becoming more 10/90 or 5/95 in several market segments, where 5% of the companies control 95% of the market. Examples of mergers like AOL and TimeWarner, Glaxo Wellcome and SmithKline Beecham, or even WorldCom and MCI, remind us daily of the behavior of giants and what a star-topology structure means for the common citizen in terms of economic networks. My interests in this matter are not to discuss the ethical values and consequences of contemporary globalization, they are based in pure scientific curiosity in the study of complex networks. However, if you are interested in this subject, you can find more information here or in the FreePress Organization website.
(1) Star topology network
I personally believe that thereâ??s a severe danger when hubs congregate an excessive number of links in any network, since the whole structure becomes extremely dependent on them and their sustainability. This problem increases even more if the lack of diversity becomes a common ground among major hubs. Hubs need to maintain themselves closer to their neighbors. Robustness is only achievable with certain precautions. It is known that under random failures/attacks scale-free networks (2) are more stable than randomly distributed networks (3), since the hubs, because of their small number, are rarely disturbed. But under a precise/intentional attack a scale-free network is highly vulnerable due to their high dependence on the vital hubs, which, if destroyed, can easily crash the entire network. Itâ??s somehow the ambiguity of scale-free networks, what makes them stronger is responsible for their main vulnerability.
I know the equilibrium point in this ambiguity is hard to unveil but I also believe is something one should pursue. This leads me to a question that has been bordering my mind lately: In terms of robustness/security can we calculate the right balance between large hubs close
r to a star-topology structure and smaller nodes closer to a randomly distributed network structure? In any approach the balance will naturally be somewhere in between, since we know both extremes are inconsistent with a scale-free network. Therefore I believe hubs should never get to a point where the network itself becomes overly dependent on them. Hubs should be closer to their smaller cousins.
(2) Scale-free Network
(3) Randomly Distributed Network
(4) If you want to understand more the importance of hubs in scale-free networks, you can read this article about error and attack tolerance in complex systems.
The element of Diversity
Hubs must be diverse in order to maintain network safety (5). Distinct hubs offer different ways of dealing and resisting to problems and difficulties. Diversity is the key element of survival in Nature, is what makes us stronger and fitter. Diversity is the key factor of genetic evolution, is what sells products as synonym of innovation and differentiation. Diversity is a central element of social, cultural and economic networks. This WIRED magazine article offers an interesting point of view about OS monoculture, the opposite condition to genetic diversity in biology. Adding to the articleâ??s argument I will quote Duncan Watts from his book Six Degrees: â??Universal software compatibility clearly confers some significant benefits on individual users. But from the perspective of system vulnerability, when everybody has the same software, everybody also has the same weaknessâ??. There will never be security or robustness in contemporary computer networks unless we reach a balanced level of diversity. Hubs should share the least common number of flaws in order to secure the network stability. Here comes my second element in the equation of Hubs Protection. In any scale-free network, hubs must be protected at all cost, in order to do so we must:
- Maintain Hubs closer to their smaller cousins (factor discussed previously)
- Maintain Hubs as diverse as possible.
(5) Spreading Virus
Copyright OrgNet. For a larger version of this image click here.
This image demonstrates how the spread of viruses, in a scale-free network, is aided by hubs â?? once a hub gets a virus it can pass it on to a very large num
ber of nodes. This particular image is a case of airborne contagion, such as SARS or TB, for more information about this image follow this link.
