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Equivalent Resistance01:16

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.
Norton Equivalent Circuits01:16

Norton Equivalent Circuits

Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent...
Norton's Theorem01:14

Norton's Theorem

Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one depicted in...
Circuit Terminology01:14

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
Protein Networks02:26

Protein Networks

An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

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Related Experiment Video

Updated: Jul 5, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
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Network 'small-world-ness': a quantitative method for determining canonical network equivalence.

Mark D Humphries1, Kevin Gurney

  • 1Adaptive Behaviour Research Group, Department of Psychology, University of Sheffield, Sheffield, United Kingdom. m.d.humphries@sheffield.ac.uk

Plos One
|May 1, 2008
PubMed
Summary

A new metric quantifies "small-world-ness" in networks, moving beyond categorical definitions. This allows for statistical testing and precise modeling using the Watts-Strogatz (WS) model, improving network analysis.

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Area of Science:

  • Network science
  • Complex systems analysis
  • Graph theory

Background:

  • Many technological, biological, and social networks exhibit 'small-world' properties, characterized by high clustering and short path lengths.
  • Current definitions of small-world networks are categorical, leading to uncertainty in classification.
  • The canonical Watts-Strogatz (WS) model is often used, but establishing an equivalent model is imprecise.

Purpose of the Study:

  • To develop a quantitative measure for 'small-world-ness'.
  • To establish a statistically testable criterion for identifying small-world networks.
  • To refine the process of assigning equivalent Watts-Strogatz (WS) models to real-world networks.

Main Methods:

  • Defined a precise metric 'S' for small-world-ness based on local clustering and path length.
  • Analyzed the behavior of 'S' across a large dataset of real-world networks.
  • Developed a method for assigning unique WS models to networks and analytically examined their properties.

Main Results:

  • Introduced a quantitative 'small-world-ness' metric (S > 1) for statistical validation.
  • Observed a consistent linear relationship between 'S' and network size (n) in real-world systems.
  • Demonstrated that associated WS models also exhibit linearity between 'S' and 'n', suggesting a common growth process.

Conclusions:

  • Quantified the concept of small-world networks with a precise metric.
  • Improved the reliability and precision of using WS canonical models for network analysis.
  • Provided a statistically robust framework for understanding and classifying small-world networks.