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Lewis Carroll's Doublets net of English words: network heterogeneity in a complex system.

Fushing H, Chen C, Hsieh YC, Farrell P - PLoS ONE (2014)

Bottom Line: Phonological communities are seen at the network level.And a balancing act between the language's global efficiency and redundancy is seen at the system level.Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.

ABSTRACT
Lewis Carroll's English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language's local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language's global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

Show MeSH
A network and its betweenness and node-to-node distance.The community geometry of the second largest clique in the 8-letter network (a) is computed from its histograms of edge betweenness (b) and node-to-node distances (c).
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pone-0114177-g003: A network and its betweenness and node-to-node distance.The community geometry of the second largest clique in the 8-letter network (a) is computed from its histograms of edge betweenness (b) and node-to-node distances (c).

Mentions: We first develop a natural and explicit measure of “distance” among all nodes, given a binary network. This distance measure not only facilitates the discovery of communities, but also induces another, implicit “distance” concept that allows us to determine whether community A is closer to community B than to community C. Thus a final computational result for a binary network is a community geometry. It then becomes clear that this community geometry reflects and mirrors many ad hoc and artificial facets of results from popular community detection methodologies, such as modularity. Furthermore, the community geometry also brings out the multiscale structural information in a network. To our knowledge, this is the first such attempt of its kind in network research. Our methodological development is illustrated here with a simple network, as shown in Fig. 3(a), which is the second largest clique of 8-letter words in our Doublets net. All of its word nodes are numbered and given in Table 3.


Lewis Carroll's Doublets net of English words: network heterogeneity in a complex system.

Fushing H, Chen C, Hsieh YC, Farrell P - PLoS ONE (2014)

A network and its betweenness and node-to-node distance.The community geometry of the second largest clique in the 8-letter network (a) is computed from its histograms of edge betweenness (b) and node-to-node distances (c).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4269387&req=5

pone-0114177-g003: A network and its betweenness and node-to-node distance.The community geometry of the second largest clique in the 8-letter network (a) is computed from its histograms of edge betweenness (b) and node-to-node distances (c).
Mentions: We first develop a natural and explicit measure of “distance” among all nodes, given a binary network. This distance measure not only facilitates the discovery of communities, but also induces another, implicit “distance” concept that allows us to determine whether community A is closer to community B than to community C. Thus a final computational result for a binary network is a community geometry. It then becomes clear that this community geometry reflects and mirrors many ad hoc and artificial facets of results from popular community detection methodologies, such as modularity. Furthermore, the community geometry also brings out the multiscale structural information in a network. To our knowledge, this is the first such attempt of its kind in network research. Our methodological development is illustrated here with a simple network, as shown in Fig. 3(a), which is the second largest clique of 8-letter words in our Doublets net. All of its word nodes are numbered and given in Table 3.

Bottom Line: Phonological communities are seen at the network level.And a balancing act between the language's global efficiency and redundancy is seen at the system level.Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.

ABSTRACT
Lewis Carroll's English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language's local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language's global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

Show MeSH