Networks are mathematical representations of systems composed of several interacting units, 
the nodes of the network. The interaction between nodes is represented by lines connecting 
them. More complex models can involve interactions that work only in one direction (from A to
B but not from B to A) and that have different weights, since some connections might be more
effective than others. Besides, the nodes themselves can have internal states that may change 
in the course of time due to interactions with the other nodes. A simple example is the Voter 
Model: a population has to decide between two candidates, red and blue. The internal state of 
a node at time t is red or blue according to the current oppinion of the individual represented 
by the node. Each individual has friends, to which it is connected, that might change its 
oppinion. Then, with probability p the node does not change its oppinion at the next time step. 
With probability (1-p) it copies the state of one of its friends. The figures below show three 
examples of distinct network topologies that might be considered: a randomly connected population;  
a scale-free population, with few highly connected nodes; and a fully connected population, 
which corresponds to the mean field approximation.


          



The theory of networks has applications in several fields: computer sciences, biology, 
highways, pipelines and power plants connections, and the social sciences. Understanding 
the topology of real networks, how they grow and die, and how their topology affects internal 
dynamical processes are some of the goals in this field. This research is a join project with 
Prof. Yaneer Bar-Yam and other researches at NECSI, and also with Paulo Guimaraes and Sergio 
F. dos Reis at the Instituto de Biologia - Unicamp.

NECSI - New England Complex Systems Institute

Recent Papers (click here for the full list)


An analytically solvable model of probabilistic network dynamics 
M.A.M. de Aguiar, I.R. Epstein and Y. Bar-Yam, Phys. Rev. E72 (2005) 67102.


Random initial condition in small Barabasi-Albert networks 
and deviations from the scale-free behavior 
Paulo R. Guimaraes Jr, Marcus A. M. de Aguiar, Jordi Bascompte, 
Pedro Jordano and Sergio Furtado dos Reis, Phys. Rev. E71 (2005) 37101.


Spectral Analysis and the Dynamic Response of Complex Networks
M.A.M. de Aguiar and Yaneer Bar-Yam, Phys. Rev. E71 (2005) 16106.

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