The paper by Réka Albert and Albert-László Barabási explores the topology of evolving networks, focusing on the impact of local events such as the addition of new nodes and links, or rewiring of existing links. They propose an extended model that incorporates these local processes to predict two fundamentally different topologies: a generalized power-law distribution and an exponential distribution. The authors develop a continuum theory to describe these regimes and derive a phase diagram that predicts the transition between them based on the relative frequency of local events. Numerical simulations support these predictions, showing that the connectivity distribution of the actor network can be accurately fit using the model. The study highlights the importance of understanding the frequency of local events in determining the large-scale topology of complex networks, suggesting potential applications in various fields such as biology, social networks, and communication networks.The paper by Réka Albert and Albert-László Barabási explores the topology of evolving networks, focusing on the impact of local events such as the addition of new nodes and links, or rewiring of existing links. They propose an extended model that incorporates these local processes to predict two fundamentally different topologies: a generalized power-law distribution and an exponential distribution. The authors develop a continuum theory to describe these regimes and derive a phase diagram that predicts the transition between them based on the relative frequency of local events. Numerical simulations support these predictions, showing that the connectivity distribution of the actor network can be accurately fit using the model. The study highlights the importance of understanding the frequency of local events in determining the large-scale topology of complex networks, suggesting potential applications in various fields such as biology, social networks, and communication networks.