Estimating the Size of Natural Networks Using Local Information

In this work, we address the problem of locally estimating the size of a natural network using local information: fitting the sum of new neighbors discovered at step of a breadth-first search (BFS) with a logarithmic function we determined as a ln(Γ(i))^e + b. With rather little computation, we reach an estimation error of at most five percent, only allowing the BFS to visit at most ten percent of the whole network. The main contributions of this work are a new approach to estimate network size with a precision higher than 95%, an estimation algorithm that can be applied in an arbitrary natural network, and an example of the use of structural properties in optimizing network algorithms.