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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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All the six minimal loop-embedded subgraphs of orders 3 and 4.They are named after Ref. [29], where 3-FFL and 4-FFL stand for three-order and four-order feed forward loops, and 3-Loop and 4-Loop mean three-order and four-order feedback loops, respectively.
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pone-0055437-g003: All the six minimal loop-embedded subgraphs of orders 3 and 4.They are named after Ref. [29], where 3-FFL and 4-FFL stand for three-order and four-order feed forward loops, and 3-Loop and 4-Loop mean three-order and four-order feedback loops, respectively.

Mentions: Figure 3 illustrates all the six different minimal loop-embedded subgraphs of orders 3 and 4. These subgraphs are named after Ref. [29] but our motivation is different from motif analysis and we adopt a different definition of subgraph (In Ref. [29] they only consider deduced subgraph). Among these six subgraphs, only Bi-fan and Bi-parallel are potential-definable. Since generally we could not obtain the explicit attributes of nodes, the homophily mechanism here only refers to the homogeneity in topology related to the potential levels. In a potential-definable subgraph, two nodes with the same potential cannot directly connect to each other and thus the homophily mechanism only works when we consider each subgraph as a whole. Specifically, a subgraph is more homogeneous if the nodes therein are of fewer potential levels. For Bi-fan the links are equivalent to each other and nodes are of two different potentials, while in Bi-parallel, links are different (two are from high-potential nodes to moderate-potential nodes, and the other two are from moderate-potential nodes to low-potential nodes) and nodes are of three different potentials. According to the assigned potentials, we could say the Bi-fan structure is more homogeneous (of fewer potential levels) than the Bi-parallel structure, then the homophily mechanism prefers the former one.


Potential theory for directed networks.

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

All the six minimal loop-embedded subgraphs of orders 3 and 4.They are named after Ref. [29], where 3-FFL and 4-FFL stand for three-order and four-order feed forward loops, and 3-Loop and 4-Loop mean three-order and four-order feedback loops, respectively.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0055437-g003: All the six minimal loop-embedded subgraphs of orders 3 and 4.They are named after Ref. [29], where 3-FFL and 4-FFL stand for three-order and four-order feed forward loops, and 3-Loop and 4-Loop mean three-order and four-order feedback loops, respectively.
Mentions: Figure 3 illustrates all the six different minimal loop-embedded subgraphs of orders 3 and 4. These subgraphs are named after Ref. [29] but our motivation is different from motif analysis and we adopt a different definition of subgraph (In Ref. [29] they only consider deduced subgraph). Among these six subgraphs, only Bi-fan and Bi-parallel are potential-definable. Since generally we could not obtain the explicit attributes of nodes, the homophily mechanism here only refers to the homogeneity in topology related to the potential levels. In a potential-definable subgraph, two nodes with the same potential cannot directly connect to each other and thus the homophily mechanism only works when we consider each subgraph as a whole. Specifically, a subgraph is more homogeneous if the nodes therein are of fewer potential levels. For Bi-fan the links are equivalent to each other and nodes are of two different potentials, while in Bi-parallel, links are different (two are from high-potential nodes to moderate-potential nodes, and the other two are from moderate-potential nodes to low-potential nodes) and nodes are of three different potentials. According to the assigned potentials, we could say the Bi-fan structure is more homogeneous (of fewer potential levels) than the Bi-parallel structure, then the homophily mechanism prefers the former one.

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