🤖 AI Summary
This study presents the first empirical examination of the competitive linking hypothesis within the Barabási-Albert network growth model. We propose a robust statistical framework to quantify node competitiveness and, integrated with complex network modeling, conduct systematic analyses of news comment and movie datasets. Our results demonstrate that perfect competition is absent in practice; instead, newly arriving nodes exhibit heterogeneous influence patterns ranging from elastic to moderate regimes. By addressing the longstanding gap in empirical validation of this competitive assumption, this work reveals the inherent heterogeneity of node influence in real-world growing networks. These findings provide critical theoretical and empirical foundations for the precise modeling of complex systems and for practical applications such as recommendation algorithms in e-commerce platforms.
📝 Abstract
Many real systems can be represented as growing networks where new nodes and links gradually emerge. The Barab\'asi-Albert model for growing networks, and many models inspired by it, are based on the idea that nodes compete for links. However, the strength and the very presence of this competition have not been tested. We propose a robust statistical approach to quantify how strongly nodes compete for links, and apply it to data from various real systems---commenting on online news and cinema attendance data. We find a range of possible behaviors, from the perfectly elastic case, where new entrants shape network growth in a way that leaves the rest of the system unaffected, to an intermediate case where new entrants measurably affect the rest. Perfect competition is never observed. These findings have direct implications for complex systems modeling and e-commerce applications.