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Related Concept Videos

Structure of Conjugated Dienes01:16

Structure of Conjugated Dienes

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Introduction
Conjugated dienes are compounds characterized by the presence of alternating double and single bonds. In a conjugated system like 1,3-butadiene, the unhybridized 2p orbital on each carbon overlaps continuously, allowing the π electrons to be delocalized across the entire molecule. In contrast, this type of overlap does not occur in cumulated and isolated dienes, such as 2,3-pentadiene and 1,4-pentadiene, respectively. Instead, the π electrons remain localized between the double...
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Structure of Benzene: Kekulé Model01:07

Structure of Benzene: Kekulé Model

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In 1865, August Kekule suggested the structure of benzene according to the structural theory of organic chemistry based on the three assertions—formula of benzene is C6H6, all the hydrogens of benzene are equivalent, and each carbon must have four bonds due to its tetravalency.
He proposed that benzene has a cyclic structure of six carbon atoms attached to one hydrogen atom each, with three alternating pi bonds.
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Diels–Alder Reaction: Characteristics of Dienes01:29

Diels–Alder Reaction: Characteristics of Dienes

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The Diels–Alder reaction brings together a diene and a dienophile to form a six-membered ring. Both components have unique characteristics that influence the rate of the reaction.
Characteristics of the diene
Conformation
The simplest example of a diene is 1,3-butadiene, an acyclic conjugated π system. At room temperature, the molecule exists as a mixture of s-cis and s-trans conformers by virtue of rotation around the carbon–carbon single bond. Although the s-trans isomer is...
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Newman Projections02:06

Newman Projections

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Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as...
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pV-Diagrams01:18

pV-Diagrams

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The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
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Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

9.0K
According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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A dandelion structure of eigenvector preferential attachment networks.

Vadood Adami1, Zahra Ebadi2, Morteza Nattagh-Najafi2

  • 1Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran. v.adami@uma.ac.ir.

Scientific Reports
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Summary

This study introduces a novel dandelion network model where agents connect based on eigenvector centrality, differing from standard preferential attachment models. This network features a super-hub and unique structural properties, offering new insights into complex network analysis.

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Area of Science:

  • Complex Networks
  • Network Science
  • Statistical Physics

Background:

  • Preferential attachment models are foundational in network science, explaining the growth of many real-world networks.
  • Existing models like Barabási-Albert do not fully capture networks with distinct hierarchical and star-like structures.

Purpose of the Study:

  • To introduce a new preferential attachment network model based on eigenvector centrality.
  • To analyze the structural and statistical properties of this novel 'dandelion network'.
  • To compare the dandelion network with existing models, such as the Barabási-Albert model.

Main Methods:

  • Development of a new network growth model where attachment probability is proportional to eigenvector centrality.
  • Analysis of network topology, including hub-and-spoke and hierarchical structures.
  • Calculation and examination of various network metrics: node degree, betweenness centrality, eigenvector centrality, community structure, clustering coefficient, shortest path statistics, and self-similarity.

Main Results:

  • The proposed dandelion network exhibits a unique super-hub agent and a distinct classification of agents based on distance to this hub.
  • The network topology is not generally scale-free, showing significant differences from the Barabási-Albert model.
  • Detailed statistical and structural analyses reveal unique properties not observed in traditional preferential attachment networks.

Conclusions:

  • The dandelion network model provides a new framework for understanding complex systems with strong central hubs and hierarchical organization.
  • Eigenvector centrality as a preferential attachment mechanism leads to distinct network properties compared to degree-based models.
  • This model offers valuable insights into the formation and structure of diverse real-world networks.