Information mobility in complex networks

Noise enhances information transfer in hierarchical networks

We study the influence of noise on information transmission in the form of packages shipped between nodes of hierarchical networks. Numerical simulations are performed for artificial tree networks, scale-free Ravasz-Barabási networks as well for a real network formed by email addresses of former Enron employees. Two types of noise are considered. One is related to packet dynamics and is responsible for a random part of packets paths. The second one originates from random changes in initial network topology. We find that the information transfer can be enhanced by the noise. The system possesses optimal performance when both kinds of noise are tuned to specific values, this corresponds to the Stochastic Resonance phenomenon. There is a non-trivial synergy present for both noisy components. We found also that hierarchical networks built of nodes of various degrees are more efficient in information transfer than trees with a fixed branching factor.

Measuring the hierarchy of feedforward networks

In this paper we explore the concept of hierarchy as a quantifiable descriptor of ordered structures, departing from the definition of three conditions to be satisfied for a hierarchical structure: order, predictability, and pyramidal structure. According to these principles, we define a hierarchical index taking concepts from graph and information theory. This estimator allows to quantify the hierarchical character of any system susceptible to be abstracted in a feedforward causal graph, i.e., a directed acyclic graph defined in a single connected structure. Our hierarchical index is a balance between this predictability and pyramidal condition by the definition of two entropies: one attending the onward flow and the other for the backward reversion. We show how this index allows to identify hierarchical, antihierarchical, and nonhierarchical structures. Our formalism reveals that departing from the defined conditions for a hierarchical structure, feedforward trees and the inverted tree graphs emerge as the only causal structures of maximal hierarchical and antihierarchical systems respectively. Conversely, null values of the hierarchical index are attributed to a number of different configuration networks; from linear chains, due to their lack of pyramid structure, to full-connected feedforward graphs where the diversity of onward pathways is canceled by the uncertainty (lack of predictability) when going backward. Some illustrative examples are provided for the distinction among these three types of hierarchical causal graphs.