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A coevolving model based on preferential triadic closure for social media networks.

Li M, Zou H, Guan S, Gong X, Li K, Di Z, Lai CH - Sci Rep (2013)

Bottom Line: The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study.In this paper, by carrying out analysis to the temporal data of Flickr and Epinions-two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks.Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, East China Normal University, Shanghai. 200241, P. R. China.

ABSTRACT
The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions-two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks. We thus proposed a coevolving dynamical model for such networks, in which the evolution is only driven by the local dynamics-the preferential triadic closure. Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.

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Comparing the properties of the model network with that of the empirical networks.The model parameters are the same as in Fig. 3. Results are averaged over 10 realizations. Numerical experiments have also been carried out for other parameters, and the results are qualitatively the same. The empirical networks are at the final stage in the data collecting window. In the Flickr network, the total users and photos are about 3.7 × 105 and 1.1 × 107, respectively. 〈kout〉 = 〈kin〉 = 50.9, 〈kf〉 = 91.7, 〈kp〉 = 3.1. In the Epinions network, the total users and reviews are about 8.7 × 104 and 1.2 × 106, respectively, where 〈kout〉 = 〈kin〉 = 9.46, 〈kf〉 = 159.9, 〈kp〉 = 11.8. (a)–(b) The degree distributions. (c)–(d) The correlations between different types of degrees associated with the same users in static network. (e)–(f) Characterizing the mean growth rate r and standard deviation σ for favorite degree. For the model network, t0 = 90,000 and t1 = 100,000. For the empirical networks, t1 is the final day in the data collecting window, and t0 is the date about 90 (400) days before t1 for the Flickr (Epinions) network.
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f4: Comparing the properties of the model network with that of the empirical networks.The model parameters are the same as in Fig. 3. Results are averaged over 10 realizations. Numerical experiments have also been carried out for other parameters, and the results are qualitatively the same. The empirical networks are at the final stage in the data collecting window. In the Flickr network, the total users and photos are about 3.7 × 105 and 1.1 × 107, respectively. 〈kout〉 = 〈kin〉 = 50.9, 〈kf〉 = 91.7, 〈kp〉 = 3.1. In the Epinions network, the total users and reviews are about 8.7 × 104 and 1.2 × 106, respectively, where 〈kout〉 = 〈kin〉 = 9.46, 〈kf〉 = 159.9, 〈kp〉 = 11.8. (a)–(b) The degree distributions. (c)–(d) The correlations between different types of degrees associated with the same users in static network. (e)–(f) Characterizing the mean growth rate r and standard deviation σ for favorite degree. For the model network, t0 = 90,000 and t1 = 100,000. For the empirical networks, t1 is the final day in the data collecting window, and t0 is the date about 90 (400) days before t1 for the Flickr (Epinions) network.

Mentions: For a complex network, the degree distribution is one of the most important statistical properties. Figs. 4(a) and 4(b) compare the degree distributions of the model with that of the empirical networks. In both cases, the distributions were calculated for the static networks at the final stage. It is shown that all the three types of degrees approximately exhibit power-law scaling, and the distributions in the model are qualitatively consistent with the counterparts of the empirical networks. In particular, the power law exponents for the social degrees and the favorite degree can be less than 2 in certain parameter regimes in the model, which are consistent with the empirical observations in many online social networks383940. If we do not consider the coevolution of dynamics and topology in the model, this property cannot be reproduced.


A coevolving model based on preferential triadic closure for social media networks.

Li M, Zou H, Guan S, Gong X, Li K, Di Z, Lai CH - Sci Rep (2013)

Comparing the properties of the model network with that of the empirical networks.The model parameters are the same as in Fig. 3. Results are averaged over 10 realizations. Numerical experiments have also been carried out for other parameters, and the results are qualitatively the same. The empirical networks are at the final stage in the data collecting window. In the Flickr network, the total users and photos are about 3.7 × 105 and 1.1 × 107, respectively. 〈kout〉 = 〈kin〉 = 50.9, 〈kf〉 = 91.7, 〈kp〉 = 3.1. In the Epinions network, the total users and reviews are about 8.7 × 104 and 1.2 × 106, respectively, where 〈kout〉 = 〈kin〉 = 9.46, 〈kf〉 = 159.9, 〈kp〉 = 11.8. (a)–(b) The degree distributions. (c)–(d) The correlations between different types of degrees associated with the same users in static network. (e)–(f) Characterizing the mean growth rate r and standard deviation σ for favorite degree. For the model network, t0 = 90,000 and t1 = 100,000. For the empirical networks, t1 is the final day in the data collecting window, and t0 is the date about 90 (400) days before t1 for the Flickr (Epinions) network.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3753589&req=5

f4: Comparing the properties of the model network with that of the empirical networks.The model parameters are the same as in Fig. 3. Results are averaged over 10 realizations. Numerical experiments have also been carried out for other parameters, and the results are qualitatively the same. The empirical networks are at the final stage in the data collecting window. In the Flickr network, the total users and photos are about 3.7 × 105 and 1.1 × 107, respectively. 〈kout〉 = 〈kin〉 = 50.9, 〈kf〉 = 91.7, 〈kp〉 = 3.1. In the Epinions network, the total users and reviews are about 8.7 × 104 and 1.2 × 106, respectively, where 〈kout〉 = 〈kin〉 = 9.46, 〈kf〉 = 159.9, 〈kp〉 = 11.8. (a)–(b) The degree distributions. (c)–(d) The correlations between different types of degrees associated with the same users in static network. (e)–(f) Characterizing the mean growth rate r and standard deviation σ for favorite degree. For the model network, t0 = 90,000 and t1 = 100,000. For the empirical networks, t1 is the final day in the data collecting window, and t0 is the date about 90 (400) days before t1 for the Flickr (Epinions) network.
Mentions: For a complex network, the degree distribution is one of the most important statistical properties. Figs. 4(a) and 4(b) compare the degree distributions of the model with that of the empirical networks. In both cases, the distributions were calculated for the static networks at the final stage. It is shown that all the three types of degrees approximately exhibit power-law scaling, and the distributions in the model are qualitatively consistent with the counterparts of the empirical networks. In particular, the power law exponents for the social degrees and the favorite degree can be less than 2 in certain parameter regimes in the model, which are consistent with the empirical observations in many online social networks383940. If we do not consider the coevolution of dynamics and topology in the model, this property cannot be reproduced.

Bottom Line: The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study.In this paper, by carrying out analysis to the temporal data of Flickr and Epinions-two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks.Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, East China Normal University, Shanghai. 200241, P. R. China.

ABSTRACT
The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions-two typical social media networks, we found that the dynamical pattern in neighborhood, especially the formation of triadic links, plays a dominant role in the evolution of networks. We thus proposed a coevolving dynamical model for such networks, in which the evolution is only driven by the local dynamics-the preferential triadic closure. Numerical experiments verified that the model can reproduce global properties which are qualitatively consistent with the empirical observations.

Show MeSH