Limits...
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.

Show MeSH
Illustration of the scores of links according to our method.The red dashed arrows are probe links. If we adopt the predictor , the scores for  and  are  ( and ) and , respectively. More examples are as follows: ▸; ▸; ▸; ▸.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3569429&req=5

pone-0055437-g006: Illustration of the scores of links according to our method.The red dashed arrows are probe links. If we adopt the predictor , the scores for and are ( and ) and , respectively. More examples are as follows: ▸; ▸; ▸; ▸.

Mentions: We design the predictors corresponding to the six minimal loop-embedded subgraphs shown in figure 3. By removing one link from every subgraph, we get twelve predictors as shown in figure 5. If we adopt the predictor , it means the score of a non-observed link is defined as the number of the th subgraphs created by the addition of this link. Notice that, a link may generate ten 3-FFLs, but their roles can be different. For example, these ten 3-FFLs may include two , three and five . So if we adopt the predictor , the score of this link is three. Therefore, if we would like to see the contribution of a link to the created 3-FFLs, we can adopt the predictor , which means that the score of a non-observed link is defined as the total number of created , and by this link, equivalent to the number of created 3-FFLs. Figure 6 illustrates a simple example about how we calculate the scores.


Potential theory for directed networks.

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

Illustration of the scores of links according to our method.The red dashed arrows are probe links. If we adopt the predictor , the scores for  and  are  ( and ) and , respectively. More examples are as follows: ▸; ▸; ▸; ▸.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055437-g006: Illustration of the scores of links according to our method.The red dashed arrows are probe links. If we adopt the predictor , the scores for and are ( and ) and , respectively. More examples are as follows: ▸; ▸; ▸; ▸.
Mentions: We design the predictors corresponding to the six minimal loop-embedded subgraphs shown in figure 3. By removing one link from every subgraph, we get twelve predictors as shown in figure 5. If we adopt the predictor , it means the score of a non-observed link is defined as the number of the th subgraphs created by the addition of this link. Notice that, a link may generate ten 3-FFLs, but their roles can be different. For example, these ten 3-FFLs may include two , three and five . So if we adopt the predictor , the score of this link is three. Therefore, if we would like to see the contribution of a link to the created 3-FFLs, we can adopt the predictor , which means that the score of a non-observed link is defined as the total number of created , and by this link, equivalent to the number of created 3-FFLs. Figure 6 illustrates a simple example about how we calculate the scores.

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