Preferential exchange: Strengthening connections in complex networks

Many social, technological, and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available concerning the structure of many networks, the strengths are more difficult to measure. Here we show that, for one particular social network, notably the e-mail network, a suitable measure of the strength of the connections can be available. We also propose a simple mechanism, based on positive feedback and reciprocity, that can explain the observed behavior and that hints toward specific dynamics of formation and reinforcement of network connections. Network data from contexts different from social sciences indicate that power-law, and generally broad, distributions of the connection strength are ubiquitous, and the proposed mechanism has a wide range of applicability.

Figure 1

Log-log representation of the e-mail distribution in five sets of folders (empty circles, full squares, and other symbols). They are remarkably similar to each other, hinting towards some form of universality. Data have been exponentially binned to reduce noise. The straight line is a power law $k^{-1.6}$.

Figure 2

Log-log representation of the e-mail distribution of two random individuals of the model, with $S_0=2$, $S=2000$, and $M_{\text{out}}=100$. The best power-law fit yields an exponent $1.8\left(2\right)$ (straight line).