Sampling from scale-free networks and the matchmaking paradox

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems Analysis

Background:

• Scale-free networks exhibit power-law degree distributions, common in real-world systems.
• Sampling subsets of nodes can lead to empirical averages that deviate from network-wide means.
• Understanding these deviations is crucial for accurate network characterization.

Purpose of the Study:

• To analyze the statistical properties of sample means in large finite scale-free networks.
• To investigate the fluctuations and skewness of empirical averages compared to the network mean.
• To explore the implications of these findings for bipartite scale-free networks, introducing the matchmaking paradox.

Main Methods:

• Mathematical analysis of degree distributions governed by power-laws (P(n) ~ n^(-1-alpha)).
• Statistical exploration of sample mean (eta) fluctuations in arbitrarily sampled node subsets (m<
• Application of derived statistics to bipartite scale-free network structures.

Main Results:

• The sample mean (eta) exhibits extremely broad and strongly skewed fluctuations around the network mean (nu=N/M).
• Typical values of the sample mean are systematically and significantly smaller than the network mean.
• In bipartite scale-free networks, sample means of the two network partitions generally differ.

Conclusions:

• Arbitrary sampling in scale-free networks yields empirical averages that are often unrepresentative of the global network properties.
• The observed systematic underestimation of the network mean has significant implications for network analysis and modeling.
• The matchmaking paradox in bipartite networks demonstrates how local sampling can reveal structural asymmetries.