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Potential theory for directed networks.

Zhang QM, Lü L, Wang WQ, Zhu YX, Yu-XiaoZhou T - PLoS ONE (2013)

Bottom Line: This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred.Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks.Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework.

View Article: PubMed Central - PubMed

Affiliation: Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, People's Republic of China.

ABSTRACT
Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.

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Illustration of the reason why Bi-fan is selected to be the final winner according to the homophily mechanism, clustering mechanism and potential theory.
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pone-0055437-g004: Illustration of the reason why Bi-fan is selected to be the final winner according to the homophily mechanism, clustering mechanism and potential theory.

Mentions: In a word, taking into account the potential theory, together with the clustering and homophily mechanisms, it is thought that the Bi-fan subgraph is the most preferred one and a link that can generate more Bi-fan subgraphs should be of higher probability to exist. This hypothesis receives strongly positive supports as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. Figure 4 illustrates the selecting procedure for the final winner Bi-fan, as well as the respective contributions of the three mechanisms.


Potential theory for directed networks.

Zhang QM, Lü L, Wang WQ, Zhu YX, Yu-XiaoZhou T - PLoS ONE (2013)

Illustration of the reason why Bi-fan is selected to be the final winner according to the homophily mechanism, clustering mechanism and potential theory.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3569429&req=5

pone-0055437-g004: Illustration of the reason why Bi-fan is selected to be the final winner according to the homophily mechanism, clustering mechanism and potential theory.
Mentions: In a word, taking into account the potential theory, together with the clustering and homophily mechanisms, it is thought that the Bi-fan subgraph is the most preferred one and a link that can generate more Bi-fan subgraphs should be of higher probability to exist. This hypothesis receives strongly positive supports as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. Figure 4 illustrates the selecting procedure for the final winner Bi-fan, as well as the respective contributions of the three mechanisms.

Bottom Line: This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred.Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks.Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework.

View Article: PubMed Central - PubMed

Affiliation: Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, People's Republic of China.

ABSTRACT
Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.

Show MeSH