The paper by Petter Holme and Beom Jun Kim introduces an extension to the standard scale-free network model, incorporating a "triad formation step" to generate networks with both a power-law degree distribution and high clustering. The authors analyze the geometric properties of these networks both analytically and numerically, finding that the model exhibits the same characteristics as standard scale-free networks, such as a power-law degree distribution and a small average geodesic length, while also maintaining high clustering. The clustering coefficient in their model is tunable through a control parameter, the average number of triad formation trials per time step. This model is more realistic for many real-world networks, which often exhibit both high clustering and scale-free nature. The authors also discuss the implications of their model for understanding network growth and the mechanisms behind the emergence of these properties.The paper by Petter Holme and Beom Jun Kim introduces an extension to the standard scale-free network model, incorporating a "triad formation step" to generate networks with both a power-law degree distribution and high clustering. The authors analyze the geometric properties of these networks both analytically and numerically, finding that the model exhibits the same characteristics as standard scale-free networks, such as a power-law degree distribution and a small average geodesic length, while also maintaining high clustering. The clustering coefficient in their model is tunable through a control parameter, the average number of triad formation trials per time step. This model is more realistic for many real-world networks, which often exhibit both high clustering and scale-free nature. The authors also discuss the implications of their model for understanding network growth and the mechanisms behind the emergence of these properties.