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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 four example graphs.Graphs (b) and (d) are potential-definable, and the numbers labeled beside nodes are example potentials. Graphs (a) and (c) are not potential-definable, and if we set the top nodes’ potential to be 1, some nodes’ potentials cannot be determined according to the constrain that a directed link is always associated with a decrease of a unit potential.
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pone-0055437-g001: Illustration of four example graphs.Graphs (b) and (d) are potential-definable, and the numbers labeled beside nodes are example potentials. Graphs (a) and (c) are not potential-definable, and if we set the top nodes’ potential to be 1, some nodes’ potentials cannot be determined according to the constrain that a directed link is always associated with a decrease of a unit potential.

Mentions: A graph is called potential-definable if each node can be assigned a potential such that for every pair of nodes and , if there is a link from to , then ‘s potential is a unit higher than . Clearly, a link is potential-definable yet a graph containing reciprocal links is not potential-definable. Figure 1 illustrates some example graphs with orders from 2 to 4, where graphs (a) and (c) are not potential-definable and graphs (b) and (d) are potential-definable. Notice that, the condition “potential-definable” is only meaningful for a very small graph since a graph consisting of many nodes is very probably not potential-definable. Although potential-definable networks are always acyclic, the directed acyclic networks [35] are usually not potential definable. For example, the feed forward loops are directed acyclic networks but not potential-definable.


Potential theory for directed networks.

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

Illustration of four example graphs.Graphs (b) and (d) are potential-definable, and the numbers labeled beside nodes are example potentials. Graphs (a) and (c) are not potential-definable, and if we set the top nodes’ potential to be 1, some nodes’ potentials cannot be determined according to the constrain that a directed link is always associated with a decrease of a unit potential.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055437-g001: Illustration of four example graphs.Graphs (b) and (d) are potential-definable, and the numbers labeled beside nodes are example potentials. Graphs (a) and (c) are not potential-definable, and if we set the top nodes’ potential to be 1, some nodes’ potentials cannot be determined according to the constrain that a directed link is always associated with a decrease of a unit potential.
Mentions: A graph is called potential-definable if each node can be assigned a potential such that for every pair of nodes and , if there is a link from to , then ‘s potential is a unit higher than . Clearly, a link is potential-definable yet a graph containing reciprocal links is not potential-definable. Figure 1 illustrates some example graphs with orders from 2 to 4, where graphs (a) and (c) are not potential-definable and graphs (b) and (d) are potential-definable. Notice that, the condition “potential-definable” is only meaningful for a very small graph since a graph consisting of many nodes is very probably not potential-definable. Although potential-definable networks are always acyclic, the directed acyclic networks [35] are usually not potential definable. For example, the feed forward loops are directed acyclic networks but not potential-definable.

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