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Social features of online networks: the strength of intermediary ties in online social media

Przemyslaw A. Grabowicz, Jose J. Ramasco, Esteban Moro, Josep Pujol, Victor M. Eguiluz

arXiv:1107.4009v2physics.soc-phcs.SI

TL;DR

The paper examines whether online interactions carry meaningful social information and whether theories of tie strength and information diffusion apply to online networks. It analyzes Twitter’s follower network, groups, mentions, retweets, and intermediary users, finding that personal interactions concentrate within groups while information diffusion favors cross-group and intermediary links.

  • Problem

    The study addresses whether online interactions are valid indicators of social activity and whether offline theories of tie strength and information diffusion apply to online networks.

  • Method

    The authors cluster Twitter’s follower network into groups and compare the locations of mention and retweet activity across internal, between-group, and intermediary links.

  • Results

    Mentions concentrate inside groups or between close groups, whereas retweets occur more often between groups and especially on links connected to users intermediate between groups.

  • Takeaways & Limitations

    The follower network contains information about where higher-quality personal interactions and information transmission occur, including the identification of information brokers.

Abstract

from arXiv · show

An increasing fraction of today social interactions occur using online social media as communication channels. Recent worldwide events, such as social movements in Spain or revolts in the Middle East, highlight their capacity to boost people coordination. Online networks display in general a rich internal structure where users can choose among different types and intensity of interactions. Despite of this, there are still open questions regarding the social value of online interactions. For example, the existence of users with millions of online friends sheds doubts on the relevance of these relations. In this work, we focus on Twitter, one of the most popular online social networks, and find that the network formed by the basic type of connections is organized in groups. The activity of the users conforms to the landscape determined by such groups. Furthermore, Twitter's distinction between different types of interactions allows us to establish a parallelism between online and offline social networks: personal interactions are more likely to occur on internal links to the groups (the weakness of strong ties), events transmitting new information go preferentially through links connecting different groups (the strength of weak ties) or even more through links connecting to users belonging to several groups that act as brokers (the strength of intermediary ties).

I. INTRODUCTION

The paper asks whether online interactions carry meaningful social information and whether offline tie theories also apply online. Using Twitter’s follower structure, it tests how personal communication and information diffusion relate to detected groups and intermediary users.

  • Offline tie theories link strong ties to within-group relations and weak ties to bridges that diffuse new information across groups.
  • Twitter separates follower connections, personal mentions, and retweets, enabling comparisons between social structure, personal communication, and information diffusion.
  • The study analyzes 2 408 534 users and 48 776 888 follower relations from Twitter data collected during November and December 2008.
  • Clustering identifies groups in the follower network, after which mentions and retweets are compared with the structural positions of their underlying follower links.
  • The analysis includes intermediary links and users belonging to multiple groups, while acknowledging that detected clusters cannot be confirmed as underlying online or offline social groups.

A. Description of the groups

The follower network contains heterogeneous, overlapping group structure rather than a characteristic group size. Although many users are unassigned, most links connect users associated with groups, especially across groups.

  • Oslom clustering was selected because it handles the full directed network, overlapping communities, bridging nodes, and users outside groups.
  • Group sizes decay slowly across three orders of magnitude and show no characteristic size; the largest group contains around 10,000 users.
  • 37.4% of users belong to no detected group, while at least one user belongs to more than 100 groups.
  • Although 37% of users are unclassified, links connected to them account for less than 6% of all links and even fewer mention or retweet links.
  • Between-group links are the most common connection type, because clustering seeks unusually dense mutual connectivity rather than maximizing internal-link proportions.

B. The strength of ties

The paper treats mention activity as an observable proxy for social-tie intensity. More exchanged, especially reciprocated, mentions indicate stronger ties because writing a targeted message requires effort.

  • Link intensity is defined as the number of mentions exchanged between two users.
  • Mentions are treated as personal communication, making mention-bearing links an approximation to social-tie strength.
  • A tie is considered stronger when users exchange more mentions, particularly when those mentions are reciprocated.
  • The proxy reflects the effort required to write a mention and address it to a single targeted user.

C. Internal links

Internal links are enriched for personal interactions, especially as mention ties become more intense or reciprocated. The follower network provides the baseline for comparing these patterns across group sizes.

  • C. Internal links: The analysis defines interaction fractions by group size and link position using the number of links with interaction i relative to the total number of such links.The notation distinguishes interaction type, position, and group-size dependence.
  • C. Internal links: Figure 3A compares the fraction of internal links across group sizes for follower, mention, and retweet links.If mentions and retweets appeared randomly over follower links, their curves would match the follower-network baseline.
  • C. Internal links: Figure 3B shows the distribution of mentions per link, while Figure 3C separates links by mention counts and reciprocity.The plotted categories include 1 non-reciprocated mention, 3 mentions, 6 mentions, and more than 6 reciprocated mentions.
  • C. Internal links: Mentions are more abundant on internal links than baseline follower relations for groups of up to 150 users.The comparison uses the follower network as the reference baseline.
  • C. Internal links: The fraction of internal links increases with mention intensity, making highly intense or reciprocated mention links more likely to be internal.Mention intensity is measured by the number of times a link is used and whether interaction is reciprocated.

D. Links between groups

Links between groups are concentrated among relatively small groups, with retweets favoring these links slightly more than the follower baseline. Mentions occur preferentially between groups with greater similarity, whereas retweets favor medium-similarity groups.

  • D. Links between groups: Between-group links occur mainly between groups containing fewer than 200 users.This pattern is reported for the group-link distributions and link fractions shown in Figure 4A–C.
  • D. Links between groups: Retweets are slightly more abundant than the follower baseline on between-group links, whereas mentions are less abundant.The comparison is made across follower, mention, and retweet link types.
  • D. Links between groups: Mentions more likely occur between close groups, while retweets occur between groups with medium similarity.Group similarity is defined by the overlap between the groups’ connections using a Jaccard index.

E. Intermediary links

Intermediary links combine internal group membership with access to another group. They attract mentions at rates similar to internal links but attract retweets more strongly than either internal or ordinary between-group connections.

  • E. Intermediary links: An intermediary link connects users sharing a group when at least one user also belongs to a different group.This definition identifies links that bridge group memberships through a user connected to multiple groups.
  • E. Intermediary links: The analysis compares link types using the ratio of links carrying interaction i to the total links in each position.The ratio is evaluated separately for mentions and retweets across internal, intermediary, and between-group links.
  • E. Intermediary links: Internal links attract more mentions and fewer retweets than between-group links.This pattern agrees with the predictions of the strength of weak ties theory.
  • E. Intermediary links: Intermediary links attract mentions as likely as internal links but retweets more often than either internal or between-group links.They combine internal placement and multiple-group connectivity, providing bandwidth and diversity.

III. DISCUSSION

Twitter’s follower network contains groups whose structure aligns with distinct interaction types: mentions concentrate within or between close groups, while retweets favor links between dissimilar groups and intermediary users. The follower network alone can identify brokers that connect multiple groups.

  • III. DISCUSSION: Mentions concentrate inside groups or between close groups, whereas retweets occur more often between dissimilar groups.The contrast matches the reported distinction between personal communication and information propagation.
  • III. DISCUSSION: Intermediary links attract retweets more strongly than internal or ordinary between-group links.Intermediary users belong to multiple groups and can acquire information in one group before targeting others.
  • III. DISCUSSION: The analysis identifies groups in Twitter’s follower network and shows that user activity correlates with the resulting group landscape.Mentions and retweets localize differently with respect to these groups.
  • III. DISCUSSION: Using only the follower network, the method identifies special users who broker information between different groups.These users are characterized by membership in multiple groups and their intermediary position.
  • III. DISCUSSION: The findings establish an online parallel to offline theories of weak ties, brokerage, closure, and the diversity-bandwidth tradeoff.The reported correspondence links personal interactions to stronger or closer ties and information diffusion to weaker or intermediary ties.

A. Description of the dataset

The dataset combines a large Twitter follower network with user activity records collected in late 2008. Its breadth and collection procedure provide coverage of more than half of Twitter’s most active users at that time, while favoring users in the largest connected cluster.

  • A. Description of the dataset: Table I summarizes the overall characteristics of the follower network and the interactions occurring on it.The caption identifies the table’s scope rather than specific values.
  • A. Description of the dataset: The collection proceeded in two stages: follower-network exploration followed by retrieval of user activity from the Twitter stream.Activity records included plain tweets, mentions, and retweets.
  • A. Description of the dataset: The follower-network search tends to detect high in-degree or out-degree users belonging to the largest connected cluster.This follows from the internal breadth-first exploration procedure and its stopping rule.
  • A. Description of the dataset: The dataset is estimated to contain information about more than 50% of Twitter’s most active users in late 2008.Twitter had fewer than 5 million registered users when the data were collected.

B. The OSLOM clustering method

OSLOM detects statistically significant clusters in the follower network by comparing observed groups with groups found in randomized networks. It uses probability estimation and local search to identify groups unlikely to arise by chance.

  • B. The OSLOM clustering method: OSLOM uses a topological approach to detect statistically significant clusters.Its null model reshuffles network connections to create randomized graphs for comparison.
  • B. The OSLOM clustering method: The method estimates each group’s probability within an ensemble of randomized graphs using optimized clustering and extreme-value statistics.Order statistics are also used to evaluate the probability of each group properly.
  • B. The OSLOM clustering method: OSLOM performs local network searches to find clusters with lower estimated probabilities in random graphs.The search explores groups that improve the estimated significance of the clustering result.
  • B. The OSLOM clustering method: The method returns clusters at the lowest hierarchical level.This is part of OSLOM’s procedure for selecting statistically unlikely groups.

Appendix A: Results with other clustering techniques

Alternative clustering methods largely reproduce the paper’s findings about where mentions and retweets occur, despite differences in algorithms, network samples, and group assignments. The appendix also examines robustness of bridging-link patterns and confirms microscopic predictions about personal interactions.

  • Robustness across clustering methods: The appendix evaluates whether activity-localization results persist when groups are detected with clustering methods other than Oslom.Infomap, Moses, Louvain, Real-time community detection, and Radatools are considered under differing graph and sampling constraints.
  • Description of the clustering methods: The selected methods represent modularity optimization, overlapping stochastic blockmodelling, directed-network approaches, and other community-detection techniques.Some methods analyze directed graphs directly, whereas Moses, Louvain, and Real-time operate on symmetrized networks.
  • Internal links: Mentions concentrate inside groups across clustering algorithms, with the effect generally disappearing for groups larger than roughly 150–5000 users.The threshold varies by algorithm, while Infomap and two of three full-network comparisons qualitatively agree with Oslom.
  • Links between groups: Retweet probabilities over bridging links rise with the number of non-shared groups, peak around 20, and then decline, while mention patterns remain consistent across clustering algorithms.The ratio-based curves for the network without hubs are consistent between the two clustering algorithms discussed.
  • Microscopic validation: Mentions occur more often between users sharing friends, consistent with mentions being personal interactions concentrated within communities.The Jaccard-similarity distribution for mentions is shifted toward higher similarity than the distributions for retweets or follower ties.
  • Methodological rationale: Oslom can identify random between-group links while disregarding them when evaluating group membership, despite many links running between groups.This supports its use for detecting overlapping communities and bridging nodes in the follower network.
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