PaperlayerView exact revision on arXiv

Source-linked AI summary

Social Resilience in Online Communities: The Autopsy of Friendster

David Garcia, Pavlin Mavrodiev, Frank Schweitzer

arXiv:1302.6109v1cs.SIphysics.soc-ph

TL;DR

The paper asks how online communities withstand changes that trigger user departures and cascades. It measures resilience with generalized k-core analysis and applies the approach to five online communities, finding distinct resilience patterns and tracking Friendster’s decline. The analysis identifies network conditions associated with shrinking communities and uses Friendster’s evolution as a case study.

  • Problem

    The paper addresses why online communities decline and how network structure relates to cascades of users leaving.

  • Method

    It uses generalized k-core decomposition to quantify resilience from network topology and applies the measure to five online communities and Friendster’s time evolution.

  • Results

    The five communities have different resilience patterns: Livejournal and Facebook are less resilient than Friendster and Orkut, while Friendster’s temporal analysis identifies shocks and periods of lower resilience.

  • Takeaways & Limitations

    Different online-community topologies respond differently to comparable environmental conditions, and Friendster’s changing resilience can be tracked through its k-core structure.

  • Takeaways & Limitations

    The resilience comparisons for some networks are constrained by dataset size and crawling bias, especially the high-degree bias in Myspace and tendrils in Facebook’s sample.

Abstract

from arXiv · show

We empirically analyze five online communities: Friendster, Livejournal, Facebook, Orkut, Myspace, to identify causes for the decline of social networks. We define social resilience as the ability of a community to withstand changes. We do not argue about the cause of such changes, but concentrate on their impact. Changes may cause users to leave, which may trigger further leaves of others who lost connection to their friends. This may lead to cascades of users leaving. A social network is said to be resilient if the size of such cascades can be limited. To quantify resilience, we use the k-core analysis, to identify subsets of the network in which all users have at least k friends. These connections generate benefits (b) for each user, which have to outweigh the costs (c) of being a member of the network. If this difference is not positive, users leave. After all cascades, the remaining network is the k-core of the original network determined by the cost-to-benefit c/b ratio. By analysing the cumulative distribution of k-cores we are able to calculate the number of users remaining in each community. This allows us to infer the impact of the c/b ratio on the resilience of these online communities. We find that the different online communities have different k-core distributions. Consequently, similar changes in the c/b ratio have a different impact on the amount of active users. As a case study, we focus on the evolution of Friendster. We identify time periods when new users entering the network observed an insufficient c/b ratio. This measure can be seen as a precursor of the later collapse of the community. Our analysis can be applied to estimate the impact of changes in the user interface, which may temporarily increase the c/b ratio, thus posing a threat for the community to shrink, or even to collapse.

1 Introduction

The paper investigates why large online social networks decline, focusing on how network topology relates to cascades of user departures and community survival. It develops a quantitative approach and applies it across several successful, failed, and declining networks, with a detailed Friendster case study.

  • Large online social networks can rapidly gain popularity yet suddenly lose many users, while the causes of decline remain insufficiently understood.
  • The study examines whether user-network topology is related to cascades of departures that threaten an online community’s integrity.
  • Social resilience describes a community’s ability to withstand external stresses and disturbances, including technological changes that threaten user engagement.
  • The paper provides a quantitative metric linking network topology with massive user departures under an assumption of rational user behavior.
  • The metric is applied to Friendster and Livejournal datasets and compared with partial datasets from Facebook, Orkut, and Myspace, followed by analysis of Friendster’s temporal decline.

2 Related work

Prior work studies social-group dynamics, individual churn, and network resilience, but this paper shifts attention to collective departure cascades across large online communities. It uses k-core decomposition to connect user-level departure effects with macroscopic network survival.

  • Research on social groups examines growth, decay, diffusion, homophily, and maintenance in online and scientific communities.
  • Individual churn research studies users’ decisions to stop using a service, including the influence of social environments and disconnection from networks.
  • Studies of user departure in social networks include analyses of engagement and departure, but some cases lack sufficient information about the communities examined.
  • Some social platforms allow users without friends to remain active, showing that social-network participation is not always necessary for using a service.
  • This paper complements individual-churn research by analyzing collective departure cascades through macroscopic social-network topology.
  • It introduces an empirical analysis of social resilience across different online social networks using k-core decomposition to relate environmental changes to departing-user cascades.

3 Social Resilience in OSN

The paper quantifies social resilience by modeling cascading departures with generalized k-core decomposition and a rational cost-benefit framework. The resulting core represents users who remain when their network benefits exceed participation costs.

  • Users’ departures can indirectly reduce their friends’ engagement, triggering further departures and potentially threatening the whole community.
  • Degree-based removals capture direct connectivity effects, but local properties alone do not measure the indirect effects caused by subsequent user departures.
  • 3.1 Quantifying Social Resilience: A k-core is a subnetwork in which every node has degree at least k, and iterative pruning captures both direct and indirect effects of departures.
  • 3.1 Quantifying Social Resilience: With a threshold of three friends, repeated pruning can reduce the network beyond the initial removals, capturing the full cascade of users left with too few connections.
  • The generalized k-core replaces degree with a property function that can represent different pruning mechanisms, while higher-order cores remain nested within lower-order cores.
  • 3.3 A rational model for OSN users: Users stay when their benefit from network connections exceeds their participation cost; under the model, the equilibrium network corresponds to the generalized k-core.
  • 3.3 A rational model for OSN users: The model approximates benefits as proportional to direct friends, implying that a participating user’s coreness must be at least c/b + 1.
  • 3.3 A rational model for OSN users: Social resilience is defined as the size of the K core remaining after users with coreness at most c/b leave.

4 Data on Online Social Networks

The study compares five online social networks using datasets that span successful, declining, and failed communities, while documenting important coverage and sampling differences. Friendster and Livejournal provide relatively high-quality coverage, whereas Facebook, Orkut, and Myspace are partial datasets with distinct sampling constraints.

  • Dataset selection: Five online social networks are analyzed to span successful, declining, and failed communities.The datasets cover Friendster, Livejournal, Facebook, Orkut, and Myspace.
  • Dataset selection: Friendster data provide a high-quality snapshot of publicly available profiles, friend lists, and interest-based groups before discontinuation.The dataset supports an analysis of Friendster’s network topology as a whole.
  • Coverage and design: Livejournal data cover more than 95% of the community, but analysis retains only reciprocal links because its social links are directed.Livejournal is a blog community in which social networking plays a secondary role.
  • Coverage and design: Orkut covers an estimated 11.3% of the community, while Myspace contains 100,000 users from a potentially biased breadth-first search sample.These datasets were included to examine platform design and sampling-bias effects, respectively.
  • Coverage and design: Facebook data are an unbiased but partial crawl designed to preserve network statistics, including the degree distribution.The crawl used a special random-walk technique.

5 Not power-law degree distributions

The analysis tests whether the five networks’ degree distributions follow power laws rather than relying on visual fits or goodness-of-fit measures alone. It rejects the power-law hypothesis for Facebook, Friendster, Orkut, and Livejournal, while Myspace provides only weak, potentially biased evidence.

  • Motivation: Power-law degree distributions matter because epidemic-style cascades, including departures, may persist without an epidemic threshold.The analysis therefore tests whether lower-law distributions offer an alternative explanation for massive cascades.
  • Testing procedure: The study uses maximum-likelihood fitting, KS statistics, and synthetic datasets to evaluate power-law hypotheses above d_min.A hypothesis is not rejected only when the KS-test p-value exceeds the significance level and enough datapoints span d_min to d_max.
  • Results: Facebook, Friendster, Orkut, and Livejournal have p-values well below reasonable significance thresholds, providing strong evidence against power-law degree distributions.The result is reported for the degree range from d_min to d_max.
  • Results: Myspace yields a KS-test p-value of 0.22, but the fitted power law explains only 0.623% of the dataset and may reflect BFS sampling bias.The authors therefore cannot fully reject the hypothesis but conclude that the dataset does not support it reliably.
  • Interpretation: Visual log-log plots can suggest power laws even when robust statistical analysis rejects them.The paper contrasts visual inspection with formal testing of the degree distributions.

6 Empirics of OSN Resilience

The empirical k-core analysis reveals substantial differences in resilience across online communities. These differences depend on the coreness threshold and are constrained by dataset completeness.

  • K-core decomposition: Friendster has more high-coreness nodes than Livejournal, whose larger low-coreness fringe implies a lower c/b is needed to keep the community together.Livejournal’s content-based interactions can generate high benefits per social link when users share interests.
  • K-core decomposition: Node coreness is a more reliable resilience estimator than degree because high-degree nodes can still belong to the network fringe.Coreness incorporates global information about a node’s position in the network, whereas degree alone does not.
  • Resilience comparison: The CCDF P(ks > K) estimates the fraction of users remaining under a cost-benefit threshold K, enabling resilience comparisons across networks.Nodes with coreness below K are removed under the corresponding c/b condition.
  • Resilience comparison: Friendster’s CCDF remains above Livejournal’s, although their comparable maximum coreness values show that resilience depends on the threshold rather than network size alone.The comparison uses the most reliable datasets for these two communities.
  • Resilience comparison: Resilience rankings can reverse across K: Livejournal is less resilient than Facebook between K = 10 and 50, while Friendster and Orkut cross at K = 60 and 200.Orkut has a larger active-node fraction for K < 60 or K > 200, whereas Friendster is more resilient within that interval.
  • Resilience comparison: Conclusions for Facebook, Orkut, and Myspace are limited by partial or biased datasets, unlike the more global findings for Friendster and Livejournal.The Myspace crawl overrepresented high-degree nodes, while Facebook’s restarting random walks may have accumulated tendrils in the 1-core.
  • Resilience comparison: Maximum coreness ranges from 74 for Facebook to 414 for Myspace, with Friendster at 304, Livejournal at 213, and Orkut at 253.These values indicate that the examined OSN can contain substantially deeper cores than earlier instant-messaging and Cyworld results.
  • Resilience comparison: At the 80% loss threshold, Facebook and Livejournal reach K close to 10, whereas Orkut and Friendster require K above 60.The authors report that topology alone does not explain the collapse of the unsuccessful communities and point to design or interface changes as possible drivers of user departure.

7 The Time Evolution of Friendster

The authors reconstruct Friendster’s temporal connectivity and relate user-entry periods to k-core resilience, identifying patterns associated with its decline. A steadily increasing cost-to-benefit threshold produces an unraveling that closely approximates the observed shutdown.

  • Temporal network construction: Friendster is divided into 12 event-time slices, each generally spanning 10 million sequential user IDs, to measure internal, past, and future connectivity.The final slice contains 7 million IDs.
  • Social growth mechanism: For early slices, mean future-connection distance is below the random-graph expectation, indicating limited temporal diffusion and reduced potential to recruit later users.The authors suggest this pattern may imply a user “expiration date” for bringing new users.
  • Resilience and decline: Users with coreness below the median threshold k̄_s = 6 are treated as being at risk of leaving, allowing resilience risk to be tracked across entry periods.The analysis samples 100,000-user-ID slices and estimates the fraction with k_s < k̄_s.
  • Resilience and decline: The fraction of at-risk users exceeds 0.5 before Friendster reaches 80 million accounts, indicating declining cohesion as newer users fail to connect to the rest of the network.Another peak occurs shortly after 22 million users, coinciding with declining popularity in the United States.
  • Resilience and decline: At the June 2010 reference point, 10 million active users correspond to nodes with k_s > 67 in the calibrated coreness-based estimate.This point represents 15% of the 68-million-user reference total, while search volume was 14%.
  • Resilience and decline: Starting with critical coreness K_t = 3 and increasing it by 6 per month, the unraveling model fits Friendster’s decline through shutdown with R^2 = 0.972.The remaining-user estimate is compared with weekly Google search volume as a proxy for active users.

8 Discussion

The discussion presents generalized k-core decomposition as an empirical measure of online social resilience and compares resilience across five social networks. It concludes that network topology alone does not explain success or failure, while noting macroscopic and modeling limitations.

  • Contributions: The study presents a generalized k-core decomposition that empirically measures social resilience through the structure of user departures.The approach connects an OSN’s environment with cascades of users leaving.
  • Cross-community findings: Across five influential OSN, successful Livejournal and Facebook are less resilient topologically than unsuccessful Friendster and Orkut.The study also reports that power-law degree distributions cannot explain large-scale departure cascades in these communities.
  • Cross-community findings: The comparison indicates that environmental conditions contribute substantially to OSN success, so topology alone cannot explain the studied success and failure histories.The authors call for future measurement of the costs and benefits associated with network participation.
  • Friendster case study: The Friendster case study finds restricted connections to future users, time-dependent departure risk, resilience shocks, and a k-core-based fit to its collapse.Active users are estimated from search volumes, although Alexa ranks or last-login data could provide more reliable validation data.
  • Limitations and extensions: The analysis is macroscopic and lacks microscopic user-activity and churn data needed to estimate individual network benefits and costs.The authors identify these data as necessary for further validation.
  • Limitations and extensions: The theoretical framework assumes monotonically increasing, convex benefits from active neighborhood size and leaves directionality and nonlinear overload effects open.Generalized k-core extensions can represent heterogeneous benefits or weighted social links.
Loading 1302.6109v1…