Six Degrees of Separation

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From the Wikipedia [1]:

"Six degrees of separation refers to the idea that, if a person is one "step" away from each person he or she knows and two "steps" away from each person who is known by one of the people he or she knows, then everyone is no more than six "steps" away from each person on Earth. Several studies, such as Milgram's small world experiment, have been conducted to empirically measure this connectedness. While the exact number of links between people differs depending on the population measured, it is generally found to be relatively small. Hence, six degrees of separation is somewhat synonymous with the idea of the "small world" phenomenon." (


By José Balsa-Barreiro, Aymeric Vié, et al. :

"In 1929, Frigyes Karinthy proposed the Theory of Six Degrees of Separation. According to him, two randomly selected individuals are potentially connected by an average sequence of six other individuals (Watts, 2003). A similar and popular myth in New York City says that someone standing in Times Square will probably meet an acquaintance in less than 20 min. The recent introduction of mobile devices, Internet applications, and social media have dramatically increased the interconnectivity of the globe in an unprecedented manner. The distance between individuals has never been lower (Shu and Chuang, 2011; Zhang and Tu, 2009).

Understanding the structure of human interconnections and their impact on economic and social activities are crucial for social sciences (Granovetter, 2005). The establishment of connections and interdependencies may yield benefits and opportunities both for businesses (Hidalgo et al., 2007) and social organizations (Bar-Yam, 2002), among others. For instance, the combination of components provided by multiple agents is the basis for the growth of economic complexity and innovation (Kauffman, 1995). In recent years, our economic system is being increasingly globalized fostering a permanent flow of goods and people across borders. This is manifested in the creation and expansion of free-trade zones such as the European Economic Area (EEA), the North American Free Trade Agreement (NAFTA), and the ASEAN-China Free Trade Area (ACFTA), which reveal the architecture of a unified global market." (

The Downsides of Interdependencies

By José Balsa-Barreiro, Aymeric Vié, et al. :

"The complexity of systems refers to the diversity and heterogeneity of behaviors at multiple scales, ranging from individuals to communities or societies at large. The addition of interdependencies increases the number of potential relationships among the system parts, enabling the emergence of new types of association and more elaborate behaviors. Interdependencies are the basis for the emergence of collective capabilities that would otherwise be unfeasible. Individuals associate with one another by coupling their behaviors to increase the space of possibilities of the whole system at a larger scale.

However, adding interdependencies has a hidden downside. The more connected a system is, the easier is for errors and unexpected detrimental behaviors to propagate across the system. Interdependencies create new paths for error propagation and may escalate the risks of malfunctions in both frequency and severity (Newman et al., 2006). Anomalies do not grow or occur linearly. Their magnitude may explode given the existence of critical masses and tipping points during networked propagation processes. Analyzing systemic failure exceeds traditional research methods that simplify reality by analyzing errors in isolation.

Material science and mechanical engineering consider this kind of failure. A mechanical structure becomes more vulnerable to future shocks when multiple loads are continuously applied to them. The structure crashes when the load forces overcome the resistance threshold of any part or material, which becomes more sensitive due to the repeated load forces. A fatigue process that results from the establishment of interdependencies among the material parts after exceeding certain thresholds explains this system failure.

A system with a great number of interdependencies can be extremely vulnerable to malfunctions, even if it does not come from the most important nodes. The chaos theory, which is inherent to complex systems, explains that small variations may entail huge changes in entire systems. Similarly, any potential malfunction can effortlessly cascade across the whole system and affect its functional behavior. Some concrete examples related to these effects are appreciated in very different kinds of systems, both with natural and human inception. Natural events such as forest wildfires or the consequences of earthquakes in some regions eventually manifest catastrophic dimensions and huge regional differences that go beyond the phenomenon itself (Balsa-Barreiro and Hermosilla, 2013)." (

More Information

  1. Small-World Network
  2. Network Theory
  3. Network Typology
  4. Scale-Free Network