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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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The influence of current status on the formation of new links in the Flickr and Epinions (in the insets) networks.(a)–(d) The cumulative functions of relative probability, κf (kf), κf (kout), κf (kin), and κin(kin), respectively, characterizing the cross correlations in the growth of degrees. For example, in (b), κf (kout) plots the cumulative probability for a user to build a new cross link given that his existing outdegree is kout. The exponents are obtained by fitting the curves averaged over different initial t0, and Δt is one day. See the text for the definitions of the triadic and non-triadic links. (e)–(f) Characterizing the localized influence among neighboring users. (e) The cumulative functions of probability for a user to build a cross link to a specific photo (review) given that u of his neighbors have already favorite-marked (commented) it. (f) The cumulative functions of relative probability for a pair of users to build a social link given that they have already shared z favorite photos (reviews). The straight lines are guide to the eye through this paper.
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f2: The influence of current status on the formation of new links in the Flickr and Epinions (in the insets) networks.(a)–(d) The cumulative functions of relative probability, κf (kf), κf (kout), κf (kin), and κin(kin), respectively, characterizing the cross correlations in the growth of degrees. For example, in (b), κf (kout) plots the cumulative probability for a user to build a new cross link given that his existing outdegree is kout. The exponents are obtained by fitting the curves averaged over different initial t0, and Δt is one day. See the text for the definitions of the triadic and non-triadic links. (e)–(f) Characterizing the localized influence among neighboring users. (e) The cumulative functions of probability for a user to build a cross link to a specific photo (review) given that u of his neighbors have already favorite-marked (commented) it. (f) The cumulative functions of relative probability for a pair of users to build a social link given that they have already shared z favorite photos (reviews). The straight lines are guide to the eye through this paper.

Mentions: The results of above empirical analysis are illustrated in Figs. 2(a)–2(d) and summarized in Table I. From Fig. 2(a), we can see that the relative probability for a user to build a favorite degree is proportional to the existing favorite degree. Interestingly, as shown in Figs. 2(b) and 2(c), the similar dependence pattern also exists for the outdegree and indegree. Moreover, the approximate linear form of the cumulative functions κ in the double-log scale indicates that the relative probability generating new degree satisfies a power law with respect to the existing degrees, which can be characterized by the positive exponent α as in κ(x) ~ xα+1 with x denoting the degree. Numerical analysis has shown that in the Flickr and Epinions networks the formation of new links correlates with all the existing degrees, i.e., the local topological status. In Table I, we listed all the characteristic exponents α by fitting the κ functions. They are all positive, between 0 and 1.25, confirming the positive correlation pattern in link growth.


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)

The influence of current status on the formation of new links in the Flickr and Epinions (in the insets) networks.(a)–(d) The cumulative functions of relative probability, κf (kf), κf (kout), κf (kin), and κin(kin), respectively, characterizing the cross correlations in the growth of degrees. For example, in (b), κf (kout) plots the cumulative probability for a user to build a new cross link given that his existing outdegree is kout. The exponents are obtained by fitting the curves averaged over different initial t0, and Δt is one day. See the text for the definitions of the triadic and non-triadic links. (e)–(f) Characterizing the localized influence among neighboring users. (e) The cumulative functions of probability for a user to build a cross link to a specific photo (review) given that u of his neighbors have already favorite-marked (commented) it. (f) The cumulative functions of relative probability for a pair of users to build a social link given that they have already shared z favorite photos (reviews). The straight lines are guide to the eye through this paper.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3753589&req=5

f2: The influence of current status on the formation of new links in the Flickr and Epinions (in the insets) networks.(a)–(d) The cumulative functions of relative probability, κf (kf), κf (kout), κf (kin), and κin(kin), respectively, characterizing the cross correlations in the growth of degrees. For example, in (b), κf (kout) plots the cumulative probability for a user to build a new cross link given that his existing outdegree is kout. The exponents are obtained by fitting the curves averaged over different initial t0, and Δt is one day. See the text for the definitions of the triadic and non-triadic links. (e)–(f) Characterizing the localized influence among neighboring users. (e) The cumulative functions of probability for a user to build a cross link to a specific photo (review) given that u of his neighbors have already favorite-marked (commented) it. (f) The cumulative functions of relative probability for a pair of users to build a social link given that they have already shared z favorite photos (reviews). The straight lines are guide to the eye through this paper.
Mentions: The results of above empirical analysis are illustrated in Figs. 2(a)–2(d) and summarized in Table I. From Fig. 2(a), we can see that the relative probability for a user to build a favorite degree is proportional to the existing favorite degree. Interestingly, as shown in Figs. 2(b) and 2(c), the similar dependence pattern also exists for the outdegree and indegree. Moreover, the approximate linear form of the cumulative functions κ in the double-log scale indicates that the relative probability generating new degree satisfies a power law with respect to the existing degrees, which can be characterized by the positive exponent α as in κ(x) ~ xα+1 with x denoting the degree. Numerical analysis has shown that in the Flickr and Epinions networks the formation of new links correlates with all the existing degrees, i.e., the local topological status. In Table I, we listed all the characteristic exponents α by fitting the κ functions. They are all positive, between 0 and 1.25, confirming the positive correlation pattern in link growth.

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
Related in: MedlinePlus