Networks in the Twenty-First Century
The degree ki of a network node i is its number of neighbors.
A power is an exponent to which a given quantity is raised, for example, x to the ath power, xa.
- Power Law
When the probability of an event is proportional to a power of some attribute of that event (e.g., its size), the probability distribution is said to be described by a power law.
Division of a set into non-overlapping subsets.
Networks have a long history in a number of fields ranging from sociology to mathematics. This article describes surge of interest in networks in the early twenty-first century (sometimes called network science), in large part driven by interest from the statistical physics community.
The study of networks has a deep history in mathematics, sociology, biology, and computer science reaching back to the 1700. But the twenty-first century is when the study of networks grew into a science in its...
KeywordsDegree Distribution Cluster Coefficient Random Network Community Detection Preferential Attachment
The author would like to thank Vedran Sekara for insightful comments on the manuscript.
- Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of 1/f noise. Phys Rev Lett 59(4):381–384. MathSciNet
- Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509. MathSciNet
- Brin S, Page L (1998) The anatomy of a large scale hypertextual web search engine. Comput Netw 30:107Google Scholar
- Milgram S (1967) The small world problem. Psychol Today 2:60Google Scholar
- Watts DJ (1999) Small worlds. Princeton University Press, PrincetonGoogle Scholar