# Complex networks and collective behavior in nature

#### Copyrigth picture

### Other web pages

- Collective animal behavior @ Princeton
- Complex human networks @ mit
- Complex systems @ UNAM
- Barabasi Lab web page

### Divulgation papers

- #### Physics Today - October 2007

  Statistical Physics is for the Birds.

- #### Book by A. Barabasi

  Linked: How Everything Is Connected to Everything Else and What It Means.

### Research papers

- #### Nature, April, 2010

  Hierarchical group dynamics in pigeon flocks.

- #### arXiv 29 Nov 2006

  Collective behavior of interacting self-propelled particles.

- #### IJMPB 23, 3661-3685 (2009)

  On the emergence of collective order in swarming systems: A recent debate.

- #### Nature Physics 2, 532 - 536 (2006)

  Effects of topology on network evolution.

- #### Nature 433, 392-395 (2005)

  Self-similarity of complex networks.

#### Introduction [1]

In the last decade there has been an intensive study of structural and dynamical properties of complex networks. This interest in complex networks is because their presence in many examples in nature. Many of them are part of our daily life and they are present at different organization levels.
For example, some biological networks that we can find at microscopic level are: genetic regulation networks, protein networks, neuronal networks and metabolic networks. On another scale, we can find information networks (e.g. internet), social networks (e. g. facebook, scientific collaborators, spread of diseases) and ecological networks. An interesting fact, is that these networks, very different in scale and nature, share similar structural properties. This very simple but surprising fact, has made possible to create mathematical models to understand and to explain the structural and sometimes dynamical properties of this networks.

The study of networks concerns different fields in science, from neurobiology to statistical physics. One of the most basic questions is about structure. why is that? Because structure always is correlated to function. how can we describe the wiring diagram of a food chain or the metabolic network of E. coli?, Are there particular characteristics or unifiying principles to describe such as different examples?. The answers to this kind of questions could give us important information about function. For example, the structure of social networks affects the spread of information and disease.

#### Collective motion in Nature

The collective motion of systems such as schools of ﬁsh, swarms of insects, or ﬂocks of birds, in which hundreds or thousands of organisms move together in the same direction without the apparent guidance of a leader, is one of the most spectacular examples of large-scale organization observed in nature [6]. From the physical point of view, there has been a drive to try to determine and understand the general principles that govern the emergence of collective order in these systems, in which the interactions between individuals are presumably of short-range. During the last 15 years, several models have been proposed to account for the large-scale properties of ﬂocks and swarms. However, in spite of many eﬀorts, the understanding of these general principles has remained elusive, partly due to the fact that the systems under study are not in equilibrium. Hence, the standard theorems and techniques of statistical mechanics that work well to explain the emergence of long range order in equilibrium systems, cannot be applied to understand the occurrence of apparently similar phenomena in large groups of moving organisms, or systems of self-propelled particles.

Why is important the study of animal collective behavior? Movement ecologists contend that their work will have practical applications such as understanding the spread of bovine tuberculosis in moving buffalo herds in South Africa. Or conservation biologists may find that proliferation of invasive species, be they viruses, weeds or goats, is governed by common rules that, once understood, could be used to prevent an invasion.
This web page attempts to present an introduction to these two related topics: structure of complex networks and the basics about models that seek to describe animal collective behavior.In the structure section some concepts and mathematical tools that have been developed in the last years to analyze the structure of complex networks are presented. In the dynamics section is shown a brief introduction to Vicsek model wich attemps to analyze collective motion of self-propelled particles. In both sections you will see pictures of these complex networks as well as some of the results that has been published to describe those. None of the images shown there was created by me, so I tried to cite the original sources to the better of my knowledge. Finally, in the references section there is a set of citations that can be useful for a more complete and formal description.