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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 twelve predictors corresponding to the subgraphs shown in figure 3.The red dashed arrows represent the links removed from the original subgraphs. The relations are as follows: {, , }  3-FFL, {}  3-Loop, {}  Bi-fan, {, }  Bi-parallel, {}  4-Loop, {, , , }  4-FFL.
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pone-0055437-g005: Illustration of the twelve predictors corresponding to the subgraphs shown in figure 3.The red dashed arrows represent the links removed from the original subgraphs. The relations are as follows: {, , } 3-FFL, {} 3-Loop, {} Bi-fan, {, } Bi-parallel, {} 4-Loop, {, , , } 4-FFL.

Mentions: Corresponding to these six subgraphs we get 12 individual predictors by removing one link from every subgraph (S1–S12, see figure 5). To evaluate the accuracy of a predictor, a network is divided into two parts – training set and testing set. Denote one pair of disconnected nodes in the network as a nonexistent link, then all links can be classified into three categories: observed links are the ones in the training set, missing links are the ones in the testing set, and nonexisting links are the remain links. All the missing links and nonexisting links constitute the set of non-observed links. A good predictor will assign higher scores to missing links than nonexistent ones. We adopt the Area under the Receiver operating characteristic Curve (AUC) to evaluate the prediction accuracy: a higher AUC value corresponds to a better predictor. Please see details about the link prediction algorithm and the evaluation metric for algorithmic performance in Methods and Materials.


Potential theory for directed networks.

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

Illustration of the twelve predictors corresponding to the subgraphs shown in figure 3.The red dashed arrows represent the links removed from the original subgraphs. The relations are as follows: {, , }  3-FFL, {}  3-Loop, {}  Bi-fan, {, }  Bi-parallel, {}  4-Loop, {, , , }  4-FFL.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055437-g005: Illustration of the twelve predictors corresponding to the subgraphs shown in figure 3.The red dashed arrows represent the links removed from the original subgraphs. The relations are as follows: {, , } 3-FFL, {} 3-Loop, {} Bi-fan, {, } Bi-parallel, {} 4-Loop, {, , , } 4-FFL.
Mentions: Corresponding to these six subgraphs we get 12 individual predictors by removing one link from every subgraph (S1–S12, see figure 5). To evaluate the accuracy of a predictor, a network is divided into two parts – training set and testing set. Denote one pair of disconnected nodes in the network as a nonexistent link, then all links can be classified into three categories: observed links are the ones in the training set, missing links are the ones in the testing set, and nonexisting links are the remain links. All the missing links and nonexisting links constitute the set of non-observed links. A good predictor will assign higher scores to missing links than nonexistent ones. We adopt the Area under the Receiver operating characteristic Curve (AUC) to evaluate the prediction accuracy: a higher AUC value corresponds to a better predictor. Please see details about the link prediction algorithm and the evaluation metric for algorithmic performance in Methods and Materials.

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