Network Sampling: From Static to Streaming Graphs (1211.3412v1)

Abstract: Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling, by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topology-based sampling. Our experimental results indicate that our proposed family of sampling methods more accurately preserves the underlying properties of the graph for both static and streaming graphs. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.

• The paper introduces graph induction techniques that maintain connectivity in sampled subgraphs, reducing bias in network analysis.
• The evaluation demonstrates superior preservation of key network metrics, such as degree and clustering coefficients, across real-world datasets.
• It highlights the trade-offs between computational complexity and sample representativeness, impacting relational classification performance.

Overview of "Network Sampling: From Static to Streaming Graphs"

The paper "Network Sampling: From Static to Streaming Graphs" by Ahmed et al. provides a comprehensive framework for the discussion and advancement of network sampling techniques. Tackling the formidable challenge posed by the vastness and evolving nature of real-world networks, the authors propose a spectrum of computational models for network sampling, extending from static to streaming scenarios. This work holds significance in understanding how smaller, representative samples can be extracted from large-scale networks while preserving essential topological characteristics.

The authors introduce an innovative family of sampling methods centered on the concept of graph induction. These approaches are capable of generalization across diverse computational models, thereby facilitating more effective sampling for both static and streaming graphs. The paper explores three predominant categories of network sampling methods: node-based, edge-based, and topology-based methods, and it illustrates how traditional static sampling techniques can be modified for use in graph streams.

Experimentation shows that the methods proposed by the authors preserve the underlying properties of graphs more accurately than existing approaches. Such an advancement is crucial not only for the general understanding of network structure but also for the specific application areas like relational classification, where research illustrates the impact of sampling on parameter estimation and classifier performance metrics.

Key Advances and Experimental Insights

1. Graph Induction Techniques: At the core of the proposed methodologies lies the use of graph induction, which ensures that sampled subgraphs maintain connectivity and other critical network properties. This leads to more representative samples that can be used in downstream analysis with reduced bias compared to other methods.
2. Performance on Real-world Networks: The experimental evaluation covers a variety of real-world datasets, highlighting the capacity of the proposed sampling methods to sustain the structural properties of the original network across static and streaming settings. The numerical results underscored the efficacy of the methods in capturing key distributions like degree, path length, clustering coefficients, and k-core decomposition more accurately than the alternative approaches evaluated.
3. Trade-offs between Complexity and Representativeness: An essential contribution of this work is exploring the trade-offs between algorithmic complexity and sample representativeness. As the network model shifts from static to streaming, achieving an effective balance becomes critical, which the proposed methods effectively demonstrate.
4. Influence on Relational Classification: The paper expands the discourse by investigating the effect of network sampling methods on the parameter estimation and evaluation of relational classification algorithms. Findings indicate that the sampling approach can substantially alter both the perceived class distributions and classifier performance outcomes.

Implications and Future Prospects

Given the increasing ubiquity of large-scale networked data, the insights provided by Ahmed et al. regarding sampling methods have significant theoretical and practical implications. The ability to efficiently sample from both static and streaming graphs enables researchers and practitioners to conduct scalable analysis, perform real-time data mining, and simulate network processes. The integration of graph induction into a streaming context opens pathways for deploying network analyses in settings that demand adaptability and low-latency processing, such as social media analytics, sensor networks, and online communications.

Future research can build on this foundational work by refining these methods to further decrease computational costs, improve their robustness in various streaming conditions, or expand their applicability to newer classes of networks, such as those characterized by hypergraphs or heterogeneous graphs. Additionally, the development of sampling techniques sensitive to specific network properties, constrained by domain-specific requirements, represents a fertile area for continued investigation.