Lecture

Networks: Structure and Properties

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In course

PHYS-435: Statistical physics III

This course introduces statistical field theory, and uses concepts related to phase transitions to discuss a variety of complex systems (random walks and polymers, disordered systems, combinatorial optimisation, information theory and error correcting cod ...

Description

This lecture covers the structure and properties of networks, focusing on topics such as dating networks, protein interactions, and neuron networks. It discusses the concept of small-world effect, hubs, and the scale-free property of networks, with examples and derivations.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Small-world experiment

The small-world experiment comprised several experiments conducted by Stanley Milgram and other researchers examining the average path length for social networks of people in the United States. The research was groundbreaking in that it suggested that human society is a small-world-type network characterized by short path-lengths. The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself.

Network theory

In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience.

Radiometric dating

Radiometric dating, radioactive dating or radioisotope dating is a technique which is used to date materials such as rocks or carbon, in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.

Chronological dating

Chronological dating, or simply dating, is the process of attributing to an object or event a date in the past, allowing such object or event to be located in a previously established chronology. This usually requires what is commonly known as a "dating method". Several dating methods exist, depending on different criteria and techniques, and some very well known examples of disciplines using such techniques are, for example, history, archaeology, geology, paleontology, astronomy and even forensic science, since in the latter it is sometimes necessary to investigate the moment in the past during which the death of a cadaver occurred.

Null graph

In the mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an "empty graph"). The order-zero graph, K_0, is the unique graph having no vertices (hence its order is zero). It follows that K_0 also has no edges. Thus the null graph is a regular graph of degree zero. Some authors exclude K_0 from consideration as a graph (either by definition, or more simply as a matter of convenience).

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