2.5K-Graphs: from Sampling to Generation

TL;DR

This paper introduces a practical methodology for generating realistic graphs that match specific network metrics, using sampling-based estimators and efficient algorithms, outperforming existing methods in speed and accuracy.

Contribution

The authors develop a complete approach combining sampling estimators, property adjustment, and topology generation to produce graphs matching joint degree distribution and clustering coefficients.

Findings

Generated graphs closely match original in multiple metrics.

Method is significantly faster than existing techniques.

Graphs preserve key structural properties of real networks.

Abstract

Understanding network structure and having access to realistic graphs plays a central role in computer and social networks research. In this paper, we propose a complete, and practical methodology for generating graphs that resemble a real graph of interest. The metrics of the original topology we target to match are the joint degree distribution (JDD) and the degree-dependent average clustering coefficient ($\bar{c}(k)$). We start by developing efficient estimators for these two metrics based on a node sample collected via either independence sampling or random walks. Then, we process the output of the estimators to ensure that the target properties are realizable. Finally, we propose an efficient algorithm for generating topologies that have the exact target JDD and a $\bar{c}(k)$ close to the target. Extensive simulations using real-life graphs show that the graphs generated by our methodology are similar to the original graph with respect to, not only the two target metrics, but also a wide range of other topological metrics; furthermore, our generator is order of magnitudes faster than state-of-the-art techniques.