Weak Links: Stabilizers of Complex Systems from Proteins to Social Networks

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Reviewed by Makany Tamas
School of Psychology, University of Southampton, UK

Recently, on my way to attend the Complex Systems Summer School organized by the Santa Fe Institute, a US customs officer at the Cincinnati International Airport asked me the purpose of my trip. With some concern in my voice I replied that I had come to study network complexity in physical, biological, social and cultural systems. Despite what must have seemed an unsatisfactory answer, the clearly puzzled officer finally granted me leave to enter the country. However, this incident made me think of how complex systems could be described and summarized in such a way that both researchers of the field and lay people, like US immigration officials, could understand the key concepts and their relevance.

In his new book, Weak Links: Stabilizers of Complex Systems from Proteins to Social Networks, the Hungarian Professor of Biochemistry at the Semmelweis University of Budapest, Peter Csermely provides an excellent example of how this could be achieved. The formula involves three simple rules. First, he explains some general terminology of network theory, such as small-worldness, self-organisation, scale-freeness, network stability or nestedness, all are essential to understand why highly diverse systems show very similar behavioural patterns. Second, each chapter discusses these basic principles in different complex systems starting at the level of atoms and molecules, followed by biological and social networks, and wrapped up with global structures such as world history and economy. Third, the language of the book is refreshing in the way it guides the reader on a stunning journey through "Net-land" as the world of complex systems is often labelled by Csermely. Even the most difficult theories are well presented with a plentiful supply of examples and neat analogies.

Throughout the book, the author provides very recent and comprehensive references for the topics. The most creditable additions are the list of URLs and the detailed glossary of the technological terms. The parts, which might at times seem rather hypothetical are usually marked by caricature notations, essentially smiles indicating certain paragraphs variously as tenuous or self-critical. They help make the book more conversational and readable.

A shortcoming of the book is that it consistently overrates some network phenomena. For instance, scale-freeness in networks is still an issue with intensive debates amongst the leading researchers of the field (Krieger 2006). The notion (often called a "power-law") refers to the property of any system, where the links between its nodes or elements could be described as an exponential probability distribution, represented as a straight line on a log-log scale.

Why are power-laws interesting to network researchers? The answer is twofold. In part it is because such a distribution is so often found in everyday life (Barabasi 2002). Examples include scientific collaborations (Newman 2001), food webs (Williams and Martinez 2000), animal foraging patterns (Viswanathan et al. 1996), world-wide web structure (Faloutsos et al. 1999) and patterns of email correspondence (Oliveira and Barabasi 2005). The other and perhaps more interesting reason why power-laws are interesting originates from the fact that unlike Gaussian or Poisson-like distributions, scale-free networks favour extreme values that increase network robustness through higher diversity. Despite these arguments, it remains doubtful whether a power-law is a meaningful property of complex systems or just fashionable hype.

The real merit of Csermely's book begins with Chapter 5, where weak links are being introduced to the reader. "A link is defined as 'weak', when its addition or removal does not change the mean value of a target measure at a statistically discernible way" (p. 83). The main argument is that weak links stabilize all complex systems. Although this may initially appear to be an over-statement, the author assembles a holistic picture with blocks of evidence from different disciplines. It begins with an insightful analysis at the atomic and molecular levels that includes a discussion about protein folding and continues with the role of weak links in cellular network stability, biological stress management, diseases and the mechanisms of aging. From the detailed descriptions and well focused presentation, it is apparent that the author has bought to bear his own background from this field as a biochemist. These chapters (Chapter 6-7-8) have the most coherent structure, and the complexity of the argument is backed up by plenty of supporting evidence.

As the line of discussion leads towards the psychological, social and cultural weak link aspects of complex systems (Chapter 8-9-10), the picture becomes messier and more hypothetical. This is undoubtedly due to the fact that network mechanisms on these higher organizational levels are less well understood. Scientific research should shed light on some of the presently hidden relationships existing within these fields. Take, for instance, an idea in Chapter 8 regarding the characterisation of "stronglinkers" versus "weaklinkers" as individual personality types. It is not clear how the author infers the notion of these traits on the basis of Bateson et al. (2004) hypothesis of "small phenotypes" versus "big phenotypes". Although analogies could play a crucial role in interdisciplinary research, without sufficient direct supporting evidence the reader might find these ideas interesting, but scientifically less valid. Nevertheless, the speculative intellectual remarks could point to further research questions that might finally prove or disprove some or all of the author's ideas.

The way Csermely describes weak links in social nets is particularly interesting (Chapter 9). Consistently with the rest of the book, he puts forward the argument that weak links determine system stability and diversity. As it has been earlier proposed by evolutionary scientists, the reason for the menopause in animal and human societies is adaptive, not only because it prevents genetic malformations due to late pregnancies, but also because the reproductive cessation of elder females or grandmothers allows them to assist the upbringing of their own grandchildren (Sherman 1998). The book places this and much more supporting empirical evidence, such as the functional role of gossiping and the higher stress-tolerance threshold of women in the broader context of social networks, and argues that women stabilise societies by acting as weak links. Although it is appealing to accept the "women–weak link" argument, one should be extremely cautious when translating this finding into the original definition. This vague statement would allow the logical fallacy of saying that the addition or removal of grandmothers in a society does not change the mean value of family relations at a statistically discernible way.

Despite the sometimes overexcited and presumptuous statements, Weak Links provides an excellent intellectual journey through "Net-land". The final chapter summarizes the effects of weak links on dynamic networks, and as the author drives us through the explanations of energy landscapes and higher level complexities, he draws his final conclusions. Complex systems, be they biological, technological or social ones, are too complex to comprehend with our limited cognitive capabilities, therefore some degree of simplification is inevitable. These systems need to be transformed into their mono-landscape equivalent with a handful of identifiable behaviours that determine the points of stability. The most suitable tool for such "complex reductionism" according to Csermely will be game theory, but it is up to future complex systems researchers to find the right ways of applying ideas from this field.

In conclusion, this book represents an excellent overview of a wide selection of complex systems research and a novel approach to understanding the relevance of weak links. It is written in an enjoyable style that makes the content accessible to readers with virtually any background, including network scientists, and even perhaps US custom officials.