[Paper Review] Evolving Twitter: an experimental analysis of graph properties of the social graph

Despoina Antonakaki, Sotiris Ioannidis+1 more|arXiv (Cornell University)|Oct 5, 2015

Complex Network Analysis Techniques34 references3 citations

TL;DR

This paper proposes a sampling framework to estimate 24 graph properties on Twitter's evolving social graph, using a heuristic to approximate edge creation times from API-sorted follower lists. It reveals three distinct growth phases—explosive, deflationary, and stable—over 2006–2015, with key metrics like centrality and transitivity declining, indicating Twitter's shift from a niche microblogging platform to a broad social medium.

ABSTRACT

Twitter is one of the most prominent Online Social Networks. It covers a significant part of the online worldwide population~20% and has impressive growth rates. The social graph of Twitter has been the subject of numerous studies since it can reveal the intrinsic properties of large and complex online communities. Despite the plethora of these studies, there is a limited cover on the properties of the social graph while they evolve over time. Moreover, due to the extreme size of this social network (millions of nodes, billions of edges), there is a small subset of possible graph properties that can be efficiently measured in a reasonable timescale. In this paper we propose a sampling framework that allows the estimation of graph properties on large social networks. We apply this framework to a subset of Twitter's social network that has 13.2 million users, 8.3 billion edges and covers the complete Twitter timeline (from April 2006 to January 2015). We derive estimation on the time evolution of 24 graph properties many of which have never been measured on large social networks. We further discuss how these estimations shed more light on the inner structure and growth dynamics of Twitter's social network.

Motivation & Objective

• To analyze the time-evolving structural properties of Twitter’s social graph, which remains underexplored despite its scale and influence.
• To address the computational infeasibility of measuring graph metrics on billion-edge networks by proposing a scalable sampling framework.
• To estimate the creation time of following relationships using a heuristic based on Twitter API’s sorted follower lists.
• To assess how user-level and network-level metrics evolve over time, revealing shifts in Twitter’s growth dynamics and structural organization.
• To enable large-scale graph analysis on real-world social networks where full computation is impractical due to memory and time constraints.

Proposed method

• Developed a heuristic to estimate the creation time of Twitter following relationships by leveraging the fact that Twitter’s API returns followers in chronological order.
• Applied a two-dimensional sampling strategy: temporal partitioning of the graph into eras based on estimated link creation times, and random sub-sampling of nodes or subgraphs for computationally heavy metrics.
• Used cutoff-based approximations for metrics like betweenness centrality to reduce time complexity while preserving accuracy.
• Measured 24 graph properties across 13.2 million users and 8.3 billion edges, covering structural, centrality, and density-based metrics.
• Split the dataset into three time periods (2006–2009, 2009–2011, 2011–2014) to analyze growth dynamics and structural evolution.
• Validated sampling accuracy by comparing sub-sampled results with full-graph metrics where feasible, ensuring reliable estimation despite reduced scale.

Experimental results

Research questions

• RQ1 How can the creation time of Twitter following relationships be estimated when not directly exposed by the API?
• RQ2 Which graph properties exhibit significant temporal evolution in Twitter’s social network over its first decade?
• RQ3 What are the dominant growth dynamics of Twitter’s social graph, and how do they change over time?
• RQ4 To what extent can random sub-sampling provide reliable approximations of large-scale graph metrics in memory-constrained environments?
• RQ5 How do user-level centrality and network-level structural properties evolve, reflecting shifts in Twitter’s role from microblogging to broader social interaction?

Key findings

• The paper identifies three distinct growth phases in Twitter’s social graph: an explosive growth phase (2006–2009), a deflationary phase (2009–2011), and a stable growth phase (2011–2014).
• Metrics such as closeness, betweenness, eigenvector centrality, and local transitivity show a consistent decline over time, indicating a shift in influence dynamics toward more distributed user engagement.
• The density and cocitation metrics also exhibit a decreasing trend, suggesting a move away from tightly-knit communities toward a more loosely connected network structure.
• The eccentricity and pagerank metrics decrease steadily, reflecting a reduction in the dominance of highly central nodes over time.
• The sampling framework successfully approximates graph metrics with acceptable accuracy, even for metrics with quadratic or higher time complexity.
• The heuristic for estimating link creation times enables temporal analysis of the social graph, which is otherwise infeasible due to missing metadata from Twitter’s API.