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arxiv: 2606.23530 · v1 · pith:5HP2ZU2Onew · submitted 2026-06-22 · 💻 cs.SI · cs.CY· physics.soc-ph

Direct and Indirect Influence on Likes in Social Media

Ivan Kozitsin , Anton V. Proskurnikov This is my paper

Pith reviewed 2026-06-26 05:49 UTC · model grok-4.3

classification 💻 cs.SI cs.CYphysics.soc-ph
keywords social influenceindirect contagiononline social networksgraph distancestructural diversityliking behaviornetwork analysis
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The pith

Activity among friends of friends is substantially associated with a user's likelihood of liking a post.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how direct and indirect social influence affects the probability that a user likes a post in an online social network. It establishes that activity at graph distances one and two from the user plays a central role, with the effect at distance two remaining even without any active direct neighbors. This points to indirect influence pathways operating through the network. The analysis also finds that the number of connected components among active friends predicts liking, while effects do not extend to distance three or beyond. These findings matter because they suggest that influence in social media can propagate through second-order connections in ways that simpler direct-tie models would miss.

Core claim

The study shows that the probability a user likes a post is most strongly associated with the presence of active nodes at distances one and two in the friendship network. The association with second-order activity persists in the absence of active direct neighbors, which is consistent with indirect influence. Nodes at distance three or more show no significant association. The number of connected components among active friends is also a significant predictor of liking behavior, supporting the structural diversity hypothesis.

What carries the argument

Graph distance to active nodes and the number of connected components in the active friends subgraph, which together capture direct, indirect, and structural aspects of network influence on liking.

If this is right

  • If the associations reflect influence, then liking can spread indirectly up to two steps away.
  • Multiple disconnected groups of active friends increase the chance of liking compared to a single connected group.
  • Influence mechanisms appear limited to local network neighborhoods of radius two.
  • Node-level attributes like degree and gender have smaller effects than local activity patterns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Platform designs that surface content from second-order neighbors could increase engagement more than focusing only on direct friends.
  • Similar distance-limited effects might be testable in other behaviors such as commenting or sharing.
  • Models of information diffusion should incorporate second-order terms for accuracy.

Load-bearing premise

The statistical links between activity at distances one and two and liking behavior are due to causal social influence mechanisms rather than homophily, selection, or unobserved confounders.

What would settle it

An experiment that randomly exposes users to different levels of second-order activity while holding direct activity and other factors constant, and checks if the liking probability changes accordingly.

read the original abstract

The present study investigates direct and indirect social contagion mechanisms in an online social network environment. Using a large-scale dataset comprising approximately 290,000 users from the VKontakte platform, we examine the factors associated with the probability that a user likes a post. Our analysis shows that, while demographic and structural characteristics of individual nodes, such as gender and degree, contribute to the observed dynamics, the strongest associations arise from activity in the user's local network. In particular, active nodes (users who have already liked the post) at distances d = 1 and d = 2 play a central role in shaping liking behavior. We find a substantial association between second-order activity and liking probability, which persists even in the absence of active direct neighbors and is consistent with indirect influence pathways in the network. No significant association is detected for nodes at distance three or beyond. The results also support the structural diversity hypothesis: the number of connected components among active friends is a significant predictor of liking.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. This paper examines direct and indirect social contagion in liking behavior on VKontakte using a dataset of about 290,000 users. It finds that active users at network distances 1 and 2 are associated with higher liking probability, with the distance-2 association persisting without active direct neighbors, suggesting indirect influence. No significant associations appear at distance 3 or greater. The number of connected components among active friends significantly predicts liking, consistent with the structural diversity hypothesis. Node characteristics like gender and degree also play roles.

Significance. If the reported associations are robust, this study adds to the understanding of how social influence propagates beyond immediate neighbors in online networks. The large-scale, distance-resolved analysis could help refine models of information diffusion and highlight the importance of second-order connections in social media dynamics.

major comments (1)
  1. [Methods and regression model] The central interpretation of the d=2 coefficient as evidence for indirect influence requires that the logistic regression controls sufficiently for homophily and selection. The abstract lists node-level controls and structural diversity but does not reference dyadic similarity measures, community fixed effects, or lagged variables that would strengthen the case against confounding. This is load-bearing for the indirect influence claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment below and outline planned revisions.

read point-by-point responses

  1. Referee: [Methods and regression model] The central interpretation of the d=2 coefficient as evidence for indirect influence requires that the logistic regression controls sufficiently for homophily and selection. The abstract lists node-level controls and structural diversity but does not reference dyadic similarity measures, community fixed effects, or lagged variables that would strengthen the case against confounding. This is load-bearing for the indirect influence claim.

    Authors: We agree that robust controls are essential for interpreting the d=2 coefficient. The logistic regression includes node-level covariates (gender, degree, and other demographics) and the number of connected components among active friends to capture structural diversity. These are designed to mitigate individual-level homophily and local selection effects. The d=2 association remains after conditioning on the absence of active d=1 neighbors, which provides additional support for indirect pathways. We do not currently include dyadic similarity measures, community fixed effects, or lagged variables. We will revise the abstract to more precisely describe the included controls, add a dedicated limitations subsection discussing potential residual confounding from homophily/selection, and note that future work could incorporate dyadic or community-level adjustments if richer data become available. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical associations from observational data

full rationale

The paper reports statistical associations from a large-scale observational dataset using regression on node-level and network-distance features. No derivation chain, first-principles prediction, fitted parameter renamed as prediction, or load-bearing self-citation is present. Central claims are direct empirical measurements of correlations, self-contained against the data without reduction to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on the abstract alone, the study relies on standard statistical association methods without introducing new free parameters, axioms beyond routine modeling assumptions, or invented entities.

axioms (1)
  • standard math Standard assumptions underlying regression or correlation analysis of binary outcomes (e.g., logistic model independence conditions)
    Implicit when reporting associations between network activity and liking probability.

pith-pipeline@v0.9.1-grok · 5701 in / 1241 out tokens · 30105 ms · 2026-06-26T05:49:57.849878+00:00 · methodology

discussion (0)

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Reference graph

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