This paper introduces a new model for generating scale-free networks with tunable clustering. The model extends the standard scale-free network model by adding a "triad formation step" that allows for the formation of triads, thereby enabling high clustering. The model is analyzed both analytically and numerically, showing that it possesses the same characteristics as the standard scale-free networks, such as the power-law degree distribution and small average geodesic length, but with the added property of high clustering. The clustering coefficient is shown to be tunable by adjusting a control parameter—the average number of triad formation trials per time step.
The model is based on the Barabási-Albert (BA) model, which is a well-known model for generating scale-free networks. In the BA model, new vertices are added to the network and connected to existing vertices with a probability proportional to their degree. The new model adds a triad formation step, where a new vertex is connected to a neighbor of the vertex it was previously connected to. This step allows for the formation of triads, which increases the clustering coefficient.
The model is shown to produce networks with a power-law degree distribution, a small average geodesic length, and a tunable clustering coefficient. The clustering coefficient is found to increase with the number of triad formation trials per time step. The model is also shown to produce networks with a logarithmic increase in average geodesic length, similar to the BA model.
The model is compared to the Watts-Strogatz (WS) model, which is another well-known model for generating small-world networks. The WS model has high clustering but lacks the power-law degree distribution, while the BA model has a power-law degree distribution but lacks high clustering. The new model combines the properties of both models, producing networks with both high clustering and a power-law degree distribution.
The model is also compared to other models for generating scale-free networks with high clustering, such as the model proposed by Klemm and Equíluz. The new model is shown to produce networks with similar properties, but with the advantage of being able to tune the clustering coefficient. The model is also shown to produce networks with a logarithmic increase in average geodesic length, similar to the BA model. The model is therefore a useful tool for generating scale-free networks with tunable clustering.This paper introduces a new model for generating scale-free networks with tunable clustering. The model extends the standard scale-free network model by adding a "triad formation step" that allows for the formation of triads, thereby enabling high clustering. The model is analyzed both analytically and numerically, showing that it possesses the same characteristics as the standard scale-free networks, such as the power-law degree distribution and small average geodesic length, but with the added property of high clustering. The clustering coefficient is shown to be tunable by adjusting a control parameter—the average number of triad formation trials per time step.
The model is based on the Barabási-Albert (BA) model, which is a well-known model for generating scale-free networks. In the BA model, new vertices are added to the network and connected to existing vertices with a probability proportional to their degree. The new model adds a triad formation step, where a new vertex is connected to a neighbor of the vertex it was previously connected to. This step allows for the formation of triads, which increases the clustering coefficient.
The model is shown to produce networks with a power-law degree distribution, a small average geodesic length, and a tunable clustering coefficient. The clustering coefficient is found to increase with the number of triad formation trials per time step. The model is also shown to produce networks with a logarithmic increase in average geodesic length, similar to the BA model.
The model is compared to the Watts-Strogatz (WS) model, which is another well-known model for generating small-world networks. The WS model has high clustering but lacks the power-law degree distribution, while the BA model has a power-law degree distribution but lacks high clustering. The new model combines the properties of both models, producing networks with both high clustering and a power-law degree distribution.
The model is also compared to other models for generating scale-free networks with high clustering, such as the model proposed by Klemm and Equíluz. The new model is shown to produce networks with similar properties, but with the advantage of being able to tune the clustering coefficient. The model is also shown to produce networks with a logarithmic increase in average geodesic length, similar to the BA model. The model is therefore a useful tool for generating scale-free networks with tunable clustering.