Analyzing the Growth of Social Networks Using Quadratic Functions to Model the Spread of Information and Influence

Chetna

doi:10.36948/ijfmr.2025.v07i05.57168

Analyzing the Growth of Social Networks Using Quadratic Functions to Model the Spread of Information and Influence

Author(s)	Dr. Chetna
Country	India
Abstract	Social networks commonly exhibit a growth pattern characterized by rapid early expansion followed by a deceleration phase as saturation occurs. Traditional models, such as exponential growth, adequately describe initial diffusion but fail to capture the nonlinear dynamics of mature networks. This paper proposes quadratic functions as a theoretical framework to model the spread of information and influence, effectively representing both acceleration and slowdown phases within social networks. Building on foundational concepts from scale-free and small-world network theories, this framework leverages quadratic regression principles to provide a flexible and realistic portrayal of network evolution. Key factors such as virality, user engagement, network topology, and initial seed size are conceptually integrated into the model to explain their roles in influencing growth trajectories. Quadratic models inherently capture the early-stage acceleration driven by virality and network effects, while also accommodating the eventual deceleration due to saturation and diminishing returns. This dual-phase representation offers a more nuanced alternative to purely exponential or logistic models, which often oversimplify either the growth or saturation processes. By advancing this theoretical perspective, the paper aims to enrich the understanding of social network dynamics, offering valuable insights for fields such as viral marketing, digital platform design, and information dissemination strategies. Future work may explore hybrid models combining quadratic and logistic elements to further refine these dynamics.
Keywords	: social networks, quadratic functions, growth models, viral marketing, influence spread, network dynamics, computational social science, scale-free networks, small-world networks.
Field	Mathematics
Published In	Volume 7, Issue 5, September-October 2025
Published On	2025-10-04
DOI	https://doi.org/10.36948/ijfmr.2025.v07i05.57168

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Analyzing the Growth of Social Networks Using Quadratic Functions to Model the Spread of Information and Influence

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