Origins of power-law degree distribution in the heterogeneity of human activity in social networks (1304.4523v1)

Abstract: The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.

• The paper shows that individual activity levels, spanning five orders of magnitude, deterministically drive the heavy-tailed degree distribution in social networks.
• The researchers apply a causal inference framework and a maximum entropy attachment model to corroborate that node connectivity correlates directly with user activity levels.
• The findings challenge traditional preferential attachment models by revealing that variations in human behavior, not interactive connections, predominantly shape network structures.

Origins of Power-Law Degree Distribution in the Heterogeneity of Human Activity in Social Networks

The paper presents a causal analysis of power-law degree distributions in social networks, focusing on the inherent heterogeneity of human activity. The power-law degree distribution, a characteristic widely observed in social networks, is attributed to the randomness of individual human actions rather than interactive models such as preferential attachment.

Key Results and Methodology

Through a detailed causal inference analysis, the researchers identify that the heavy-tailed distribution of nodes' degrees in social networks can be traced back to the equally skewed distribution of human activity. This pattern is visible across different platforms, such as Wikipedia and the social news aggregator news2.ru. Notably, the paper finds that the degree of connectivity for an individual in a social network is primarily determined by the scale of their activity, modeled according to a "maximum entropy attachment" (MEA) framework. Here, the degree is essentially random beyond its mean, which correlates directly with the activity volume.

The analysis covered several datasets with actions spanning around five orders of magnitude. The researchers examined two properties: user activity (such as posts or messages) and the resulting degree (the number of connections established by others towards the user). By examining the correlation between these elements, the authors contribute to a nuanced understanding of how network characteristics emerge from individual behavior patterns.

Analysis and Theoretical Implications

The core hypothesis—activity deterministically affecting the mean degree—introduces the notion that the volume and intensity of an individual's activities significantly impact network structure. This premise deviates from traditional interactive models, such as preferential attachment, which focus on node connectivity driving further connections. Instead, the constants observed in maximum entropy attachment suggest that degree distribution reflects inherent individual activity levels rather than external interactions.

The proposed model successfully anticipates the parameterization of these distributions through mathematical derivations, indicating that minor variations in degree distributions across datasets can be explained predominantly by variations in human activity distributions. The paper further supports its argument with a rigorous statistical fit to geometric distributions, emphasizing the robustness of the MEA model.

Implications and Future Directions

This paper shifts the analytical focus from network interactions to individual activities in understanding social network structures. As such, it introduces a paradigm where heterogeneity in social connectivity may be accounted for predominantly by variations in individual commitment to networked platforms. The findings imply that future network analysis could benefit from centering human activity variance, broadening the scope beyond the predominantly interaction-focused theories.

Going forward, this perspective may open new avenues for understanding large-scale collaborative environments and may refine predictive models of network growth by integrating human behavioral elements as fundamental parameters. For AI developments, incorporating these insights can enhance the agent-based simulations in understanding and predicting social network dynamics, precipitating in more effective algorithms for social media platforms and collaborative tools.

Overall, the paper presents a compelling deterministic activity-based explanation for power-law degree distributions, reinforcing the need to consider individual-based drivers in network dynamics research.