[Paper Review] Connectivity in Social Networks

Sieteng Soh, Gongqi Lin+1 more|arXiv (Cornell University)|Jun 10, 2015

Benford’s Law and Fraud Detection16 references3 citations

TL;DR

This paper proposes using Benford's law as a statistical test to validate the trustworthiness of connectivity statistics in social networks, particularly to detect fake or dormant nodes. By analyzing both symmetric and asymmetric networks, the authors demonstrate that random accumulation processes converge more closely to Benford's distribution, enabling distinction between purely random and dependency-influenced network growth processes.

ABSTRACT

The value of a social network is generally determined by its size and the connectivity of its nodes. But since some of the nodes may be fake ones and others that are dormant, the question of validating the node counts by statistical tests becomes important. In this paper we propose the use of the Benford's distribution to check on the trustworthiness of the connectivity statistics. Our experiments using statistics of both symmetric and asymmetric networks show that when the accumulation processes are random, the convergence to Benford's law is significantly better, and therefore this fact can be used to distinguish between processes which are randomly generated and those with internal dependencies.

Motivation & Objective

• To assess the reliability of node connectivity statistics in social networks, especially when nodes may be fake or inactive.
• To address the challenge of validating network size and connectivity in the presence of potentially untrustworthy data sources.
• To develop a statistical method that distinguishes between random network growth and processes with internal dependencies.
• To evaluate whether Benford's law can serve as a robust indicator of data integrity in network statistics.

Proposed method

• The authors apply Benford's law to the leading digits of connectivity statistics from both symmetric and asymmetric social networks.
• They simulate random accumulation processes to generate network data under controlled conditions.
• The convergence of observed digit frequencies to Benford's distribution is measured using statistical goodness-of-fit tests.
• The method compares convergence rates between purely random processes and those with internal dependencies.
• The analysis is performed on real and synthetic network datasets to evaluate robustness across network types.
• The study uses visual and quantitative comparisons to assess how well different processes align with Benford's law.

Experimental results

Research questions

• RQ1 Can Benford's law be used to detect anomalies in social network connectivity statistics?
• RQ2 How does the convergence to Benford's distribution differ between random and dependency-influenced network growth processes?
• RQ3 To what extent does the distribution of leading digits in network connectivity data reflect the underlying data generation process?
• RQ4 Does the method reliably distinguish between random and structured network formation mechanisms?
• RQ5 How effective is Benford's law in identifying potentially fake or dormant nodes in social networks?

Key findings

• Random accumulation processes in network formation show significantly better convergence to Benford's distribution than processes with internal dependencies.
• The degree of convergence to Benford's law serves as a reliable indicator of whether network data stems from a random or structured process.
• Symmetric and asymmetric networks both exhibit improved alignment with Benford's law under random accumulation, suggesting broad applicability.
• Networks generated with internal dependencies deviate more noticeably from Benford's distribution, enabling detection of non-random behavior.
• The statistical test based on Benford's law effectively differentiates between purely random processes and those influenced by hidden dependencies.
• The method provides a practical, data-driven approach to validate the trustworthiness of connectivity statistics in social networks.