Cadmus

The New Sciences of Networks & Complexity: A Short Introduction

Abstract
This paper is the result of two recent e-workshops organized by The World Academy of Art and Science (WAAS), one on the Science of Networks, the other on Complexity. These Sci­ences have emerged in the last few decades and figure among a large group of ‘new’ sciences or knowledge acquisitors. They are connected with one another and are very well exposed in the diagram available under the name ‘Map of Complexity Science’ on Wikipedia. Networks exist in extremely diverse contexts: in the biological world, in social constructions, in urbanism, climate change and many more. The novelty appears in the correlations and the laws (e.g. power laws), which were discovered recently, and indicates a totally different appraisal from what was generally expected to exist. The Science of Complexity is directly related to networks. Networks are an essential part of the complexity phenomenon. Their applications, which are highly diverse, are recommended by several scientists; decision makers and politicians have to make use of this knowledge for better evaluation of the impact of their decisions in increasingly complex societies and as a function of time. The paper mentions a recent report on Complexity in Economics and the Economic Complexity Index.


1. Preamble & Frame
Networks and complexity have been recognized since quite a few decades. In recent years, real breakthroughs have taken place with the help of newmathematical instruments. Other ‘new sciences’ have emerged, say in about half a century, as illustrated by the comprehensive diagram published in Wikipedia;1 the diagram comes from a book by Brian Castellani and Frederic Hafferty2 titled Sociology and Complexity Science: A New Field of Inquiry (2009), and is called the Map of Complexity Science. It was a helping hand for drafting this paper, and is further highly recommended to be consulted. A multitude of new knowledge ‘providers’ have shown new ways and insights for exploring entities, ensembles and behavior of groups in very different domains. According to the diagram, quite a number of new sciences have emerged since the mid-20th century: the essential pillars for new ideasare Systems Theory,3 Cybernetics4 and Artificial Intelligence; a series of specific approaches emerge from there.

Cybernetics plays a central role in the acquisition of new or additional knowledge. Merriam-Webster defines the term this way:

“Cybernetics is the science of communication and control theory that is concerned especially with the comparative study of automatic control systems (as the nervous system and brain and mechanical-electrical communication systems).”

According to the diagram, the Science of Complexity was preceded and followed directly or in parallel by a series of new methods and approaches such as self-organization/autopoiesis, New Sciences of Networks and Global Network society. Not to forget the importance of the Dynamics of Systems Theory in which Jay Forrester of MIT occupies a major role which led to the publication of The Limits to Growth(1972),the first report to the Club of Rome.5

We all agree that our societies evolve to more complex entities; the evolution is expressed by economic globalization, planetary communications – wired and wireless – geopolitical conflicts, and the like. However, the decision processes at the political and societal levels continue to rely on habits and practices from ancient times: the rule of thumb method is still used in decision processes. The linear analysis in decision processes still remains the most used approach in management and governance questions, although we are aware of the complexity of societal situations. Therefore, the new sciences,6, 7 in particular networks and complexity, provide excellent new methods for analysis and prospective insights. As a matter of fact, we may treat networks as patterns or structures but complexity is an implicit property of such structures.

Focusing on New Sciences looks to be a very promising endeavor, in particular for WAAS. Although the field of these new ‘knowledge producers’ is extremely broad, it provides new understandings, and establishes specific relationships between actors in many branches of sciences and contributes beyond present assumptions.

The New Sciences are to be understood as complementary to the ‘classical’ sciences; they ‘uncover’ new relationships, new laws (of mathematical character), and new characteristics among the parameters. The new sciences enable us to take non-linear relationships within systems into account, which was almost impossible before.

There are several fundamental problems where the applications of the Sciences of Networks & Complexity provide new insights in pure scientific domains, for example in the functioning of metabolisms in micro-organisms; applications in the domain of climate change and eco-biosphere are expected to bring a better understanding on the regional and planetary scale. In the fields of sociology and economics, these problems include new methods which enhance diagnostics that were not available before.

The governance of complex industrialized societies requires a better understanding of their underlying trends and institutional political decision processes. The methods applied so far do not appear to be able to provide appropriate guidelines. New insights into the organiza­tion of very large institutions, ministries and businesses, of international governing bodies, and perhaps in the governance of financial world, etc. require approaches which the science of networks and complexity can offer.

For long, scientists have expressed the need for cross-domain analyses, overcoming the exclusive approach of specialized understanding and arriving at an overarching understanding, denominated as a holistic methodology. The Western science and culture of the Renaissance have made tremendous progress based on reductionist analytical methods. However, these assumptions are frequently insufficient for a deeper understanding of reality. The well-known phrase ‘The whole is more than the sum of the parts’ (attributed to Aristotle) is not only correct but now much more practicable than a reductionist approach. With the emergence of the Systems Theory, Complexity Science and related methods, a holistic understanding is at reach.

2. The Science of Networks
Several models of networks8 have been described over time: Random Network known as the Erdös-Rényi Model9 (1959); Scale-Free Model known as the BA Model called after Barabasi & Albert10, 11 (1999); Small World Model known as the Watts-Strogatz algorithm12(2008).

It must be stressed that mathematical tools have contributed substantially to analyses of the descriptions, characteristics and properties of networks, thus contributing to an understanding of reality which is yet to be recognized.

2.1 Scale-Free Networks and Power Law13, 14
Over the past few years, investigators from a variety of fields have discovered that many networks – from the World Wide Web to a cell’s metabolic system to actors in Hollywood –are dominated by a relatively small number of nodes that are connected to many other nodes.

Networks containing such important nodes or hubs tend to be what is called “scale-free” in the sense that a lower number of hubs has higher links and many nodes have less number of links. The surprising discovery was that these networks do not behave in the expected random behavior, which is a generally accepted description of phenomena in physics, result­ing frequently in the well-known ‘bell’ curve coming from a usual statistical distribution, characterized by log-log relationships which form the ‘power law’.

It is important that the scale-free networks behave in certain predictable ways: for example, they are remarkably resistant to accidental failures but extremely vulnerable to coordinated attacks.

As an example, counting how many webpages have exactly k links showed that the distribution followed a so-called power law: the probability that any node is connected to k other nodes is proportional to 1/kn. The value of n for incoming links is approximately 2. Power laws are quite different from the bell-shaped distributions that characterize random networks. Specifically, a power law does not have a peak like a bell curve does (Poisson distribution), but is instead described by a continuously decreasing function. When plotted on a log-log scale, a power law is a straight line. In contrast to a ‘democratic’ distribution of links seen in random networks, power laws describe systems in which a few hubs dominate.

2.2 Some Important Properties of Networks

2.2.1 Resilience /Robustness15

As humanity becomes increasingly dependent on electricity grids and communication webs, a much-voiced concern arises: Exactly how reliable are these types of networks? The good news is that complex systems can be amazingly resilient against accidental failures. In fact, although hundreds of routers routinely malfunction on the Internet at any moment, the network rarely suffers major disruptions. A similar degree of robustness characterizes living systems: people rarely notice the consequences of thousands of errors in their cells, ranging from mutations to misfolded proteins.

What is the origin of this robustness? Intuition tells us that the breakdown of a substantial number of nodes will result in a network’s inevitable fragmentation. This is certainly true for random networks: if a critical fraction of nodes is removed, these systems break into tiny, non-communicating islands.

Yet, simulations of scale-free networks tell us a different story: as many as 80 percent of randomly selected Internet routers can fail and the remaining ones will still form a compact cluster in which there will still be a path between any two nodes.

It is equally difficult to disrupt a cell’s protein-interaction network: measurements indicate that even after high levels of random mutations are introduced, the unaffected proteins will continue to work together.

In general, scale-free networks display an amazing robustness against accidental fail­ures, a property that is rooted in their inhomogeneous topology. The random removal of nodes will take out the small ones mainly because they are much more plenty than hubs. And the elimination of small nodes will not disrupt the network topology significantly, because they contain few links compared with the hubs, which connect to nearly everything. But a reliance on hubs has a serious drawback: vulnerability to attacks.

In a series of simulations, it was found that the removal of just a few key hubs from the Internet splintered the system into tiny groups of hopelessly isolated routers. Similarly, knockout experiments in yeast have shown that the removal of the more highly connected proteins has a significantly greater chance of killing the organism than the deletion of other nodes. These hubs are crucial; if mutations make them dysfunctional, the cell will most likely die.


1. Brian Castellani, “Complexity Map Overview,” Wikipedia http://en.wikipedia.org/wiki/File:Complexity-map-overview.png
2. Brian Castellani and Frederic Hafferty, Sociology and Complexity Science: A New Field of Inquiry (New York: Springer, 2009)
3. Immanuel Wallerstein, World-Systems Analysis: An Introduction (Durham: Duke University Press, 2004)
4. Merriam-Webster Online, http://www.merriam-webster.com/dictionary/cybernetics
5. Donella H. Meadows et al., The Limits to Growth (New York: Universe Books, 1972)
6. Melanie Mitchell, Complexity: A Guided Tour (Oxford: Oxford University Press, 2009)
7. Roger Lewin, Complexity: Life at the Edge of Chaos (London: Phoenix paperbacks, 1993)
8. M. E. J. Newman, “The Structure and Function of Complex Networks” http://arxiv.org/pdf/condmat/0303516.pdf
9. Stefano Boccaletti et al., “Complex Networks: Structure and Dynamics,” Elsevier, Physical Reports 424, no. 4-5 (2006): 175-308
10. Albert-László Barabási, Linked: The New Science of Networks (Cambridge: Perseus Publishing, 2002)
11. Albert-László Barabási and Eric Bonabeau, “Scale-Free Networks,” Scientific American 288, no. 5 (2003): 50-59 http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200305-01_SciAmer-ScaleFree/200305-01_SciAmer-ScaleFree.pdf
12. Duncan J. Watts, Six Degrees: The Science of a Connected Age (New York: W.W. Norton, 2003)
13. “Report on: Applications of Complexity Science for Public Policy: New Tools for Finding Unanticipated Consequences and Unrealized Opportunities,” OECD http://www.oecd.org/sti/sci-tech/43891980.pdf
14. Gérard Weisbuch and Sorin Solomon, eds., Tackling Complexity in Science: General Integration of the Application of Complexity in Science (Gloucester: Renouf Publishing Company Limited, 2007)
15. Barabási and Bonabeau, “Scale-Free Networks”


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