Source-linked AI summary
Characterizing and Modeling the Dynamics of Activity and Popularity
Peng Zhang, Menghui Li, Liang Gao, Ying Fan, Zengru Di
TL;DR
The paper investigates how user activity and item popularity coevolve in social media networks, an interaction not captured by studying either dynamic alone. It analyzes four empirical networks and develops a two-step random-walk model, finding rich-get-richer patterns and qualitative agreement between modeled and empirical distributions.
Problem
The paper addresses the limited understanding of how interdependent user activity and item popularity coevolve in social media networks.
Method
The authors analyze Amazon, Flickr, Delicious, and Wikipedia, then model link growth using two-step random walks.
Results
Cross links favor active users and popular items, inactive users trace popular items more strongly, and the model qualitatively reproduces empirical activity and popularity distributions.
Takeaways & Limitations
The findings clarify micro-dynamics of user activity and item popularity within the studied social media networks.
Takeaways & Limitations
The model is only qualitatively consistent with empirical results because it simplifies activation and item-access mechanisms.
Abstract
from arXiv · showhide
Social media, regarded as two-layer networks consisting of users and items, turn out to be the most important channels for access to massive information in the era of Web 2.0. The dynamics of human activity and item popularity is a crucial issue in social media networks. In this paper, by analyzing the growth of user activity and item popularity in four empirical social media networks, i.e., Amazon, Flickr, Delicious and Wikipedia, it is found that cross links between users and items are more likely to be created by active users and to be acquired by popular items, where user activity and item popularity are measured by the number of cross links associated with users and items. This indicates that users generally trace popular items, overall. However, it is found that the inactive users more severely trace popular items than the active users. Inspired by empirical analysis, we propose an evolving model for such networks, in which the evolution is driven only by two-step random walk. Numerical experiments verified that the model can qualitatively reproduce the distributions of user activity and item popularity observed in empirical networks. These results might shed light on the understandings of micro dynamics of activity and popularity in social media networks.
Introduction
Social media networks couple user activity and item popularity through interdependent cross links, yet their coevolution was not clearly understood. The paper characterizes this evolution across four networks and proposes a two-step random-walk model.
- User activity and item popularity are interdependent perspectives of cross links, so studying either dynamic alone is insufficient.
- Existing research had examined activity and popularity dynamics separately, leaving their coevolution insufficiently characterized.
- The study analyzes activity and popularity evolution in Amazon, Flickr, Delicious, and Wikipedia.
- Cross-link creation favors active users and acquisition favors popular items, while inactive users trace popular items more strongly than active users.
- The proposed evolving model uses two-step random walks and qualitatively reproduces empirical user-activity and item-popularity distributions.
Materials and Methods
The study represents social media as two-layer user–item networks and measures activity, popularity, social connections, and preferential attachment from temporal cross-link data. It also defines contribution ratios to assess how users with different activity levels pursue popular items.
- Network representation: The data are modeled as two-layer networks with users, items, social links, and user–item cross links.The social adjacency matrix S captures user–user links, while C captures user–item interests.
- Degree definitions: User activity ka counts items of interest, item popularity kp counts interested users, and social degree ks counts friends.ka and kp provide two perspectives on the cross links between users and items.
- Preferential attachment: Preferential attachment is measured by the relative probability that a new cross link connects to a user or item with degree kT at time t0.The method compares nodes acquiring new cross links during a short interval with all nodes having degree kT at t0.
- Preferential attachment: Cumulative functions are used instead of Π(kT) to smooth noisy data, with kT representing either activity degree ka or popularity degree kp.This cumulative formulation has also been used to examine preferential attachment in empirical and theoretical evolving networks.
- Contribution ratios: Absolute contribution measures new cross links from users of degree ka during a short interval relative to the total cross-link count at t0.For links directed to items of degree kp, Aka(kp) counts new links created by users with degree ka during Δt.
- Contribution ratios: The relative contribution ratio normalizes links from users with degree ka to items of degree kp by those users’ absolute contribution, indicating pursuit of popular items.This breakdown compares how often users with different activity degrees attach to items with specified popularity.
Results
The study examines how existing user activity and item popularity shape new cross-link formation in four social media networks, then models the observed dynamics with two-step random walks. Empirical results show preferential creation and attachment, with inactive users tracing popular items more strongly than active users; simulations qualitatively reproduce observed degree distributions.
- Empirical Analysis to Temporal Data: The analysis treats user-item systems as two-layer social media networks and focuses on how existing states affect new cross-link formation.The empirical networks include Amazon, Flickr, Delicious, and Wikipedia.
- Empirical Analysis to Temporal Data: Relative probabilities of existing users creating links and existing items acquiring links increase with activity degree and popularity degree, respectively.These relationships are characterized using cumulative relative-probability functions κ(ka) and κ(kp).
- Empirical Analysis to Temporal Data: Inactive users trace popular items more strongly than active users, while unpopular items attract relatively greater interest from active users.In Wikipedia, the reported slope is 2.2 for ka ≤10 versus 1.75 for ka > 10000; differences are smaller in Amazon.
- Empirical Analysis to Temporal Data: Relative contribution ratios show active users contribute above average to unpopular items but below average to popular items, with inactive users generally showing the opposite pattern.The opposite behavior has an exception in Amazon, and large-kp fluctuations can reflect low statistics.
- Modeling: The proposed evolving model uses two-step random walks to activate users and connect them with items, avoiding the need for global degree information.The model is motivated by observed social influence and friend-mediated access to items.
- Modeling: Simulations qualitatively reproduce empirical activity and popularity distributions, while parameters n, q, and m influence different degree distributions.Popularity depends on n and q, activity is strongly affected by n, and social-degree distributions are nearly independent of n and q.
Discussion
Across four empirical networks, activity and popularity follow rich-get-richer patterns, while inactive users trace popular items more intensely than active users. A two-step random-walk model qualitatively reproduces the observed distributions, but its simplifications limit quantitative agreement.
- Users and items follow rich-get-richer growth patterns in activity and popularity, respectively.
- Inactive users contribute more than average to popular items, whereas active users contribute more than average to unpopular items.
- The proposed evolving model uses a two-step random walk to reproduce empirical activity and popularity distributions qualitatively.
- The model’s quantitative mismatch reflects simplifications, including activation and item access through only specified two-step walks via friends.Empirical growth can also reflect occasional events, alternative access channels, and item attributes such as award-winning status.