Preferential attachment with partial information

TL;DR

This paper introduces a preferential attachment network growth model where new nodes have partial information, revealing how bounded and unbounded information affect degree distribution and network evolution.

Contribution

It presents a novel model incorporating partial information in network growth, showing how information bounds alter degree distribution and network properties.

Findings

Bounded information introduces an exponential tail in degree distribution.

Unbounded information allows network growth similar to the Barabási-Albert model.

Even with vanishing known node fraction, the network behaves as in the standard model.

Abstract

We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution by introducing an exponential tail, while it preserves a power law behaviour over a finite small range of degrees. On the other hand, unbounded information is sufficient to let the network grow as in the standard Barab\'asi-Albert model. Surprisingly, the latter feature holds true also when the fraction of known nodes goes asymptotically to zero. Analytical results are compared to direct simulations.