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Updated: Jun 24, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
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Topological relations between three-periodic nets. II. Binodal nets.

Vladislav A Blatov1, Davide M Proserpio

  • 1Samara State University, Ac. Pavlov St. 1, Samara 443011, Russia. blatov@ssu.samara.ru

Acta Crystallographica. Section A, Foundations of Crystallography
|April 8, 2009
PubMed
Summary
This summary is machine-generated.

Researchers discovered 38,304 novel network topologies using the TOPOS program, aiding in the identification of new materials. A new method was developed to classify node local structures, leading to the discovery of unique binodal-quasi-uninodal nets.

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Area of Science:

  • Crystallography
  • Materials Science
  • Network Theory

Background:

  • Reticular chemistry utilizes network structures to design materials.
  • Understanding network topology is crucial for predicting material properties.
  • Databases like the Reticular Chemistry Structure Resource (RCSR) catalog known frameworks.

Purpose of the Study:

  • To systematically generate and catalog novel network topologies.
  • To develop a new invariant for classifying local node environments.
  • To identify occurrences of these novel topologies in existing crystal structures.

Main Methods:

  • Utilized the TOPOS program package to generate subnets of binodal nets.
  • Sourced initial nets from the Reticular Chemistry Structure Resource (RCSR) database.
  • Developed and applied a novel invariant: the adjacency matrix of the shell graph of a node.
  • Analyzed 4604 organic and metal-organic frameworks for topological matches.

Main Results:

  • Generated and cataloged 38,304 novel binodal net topologies, stored in the TTD collection.
  • Introduced a new invariant to effectively distinguish node local topology.
  • Discovered the first six examples of binodal-quasi-uninodal nets.
  • Identified occurrences of generated topologies, including edge-transitive nets and previously unknown structures, within analyzed crystal frameworks.

Conclusions:

  • The systematic generation of network topologies reveals a vast unexplored chemical space.
  • The proposed invariant provides a powerful tool for topological classification.
  • Novel network topologies are present in known crystal structures, suggesting potential for new material discovery.