Networks in the TwentyFirst Century
Synonyms
Glossary
 Degree

The degree k_{i} of a network node i is its number of neighbors.
 Power

A power is an exponent to which a given quantity is raised, for example, x to the ath power, x^{a}.
 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.
 Partition

Division of a set into nonoverlapping subsets.
Definition
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 twentyfirst century (sometimes called network science), in large part driven by interest from the statistical physics community.
Introduction
The study of networks has a deep history in mathematics, sociology, biology, and computer science reaching back to the 1700. But the twentyfirst century is when the study of networks grew into a science in its...
Keywords
Degree Distribution Cluster Coefficient Random Network Community Detection Preferential AttachmentNotes
Acknowledgments
The author would like to thank Vedran Sekara for insightful comments on the manuscript.
References
 Ahn Y, Bagrow J, Lehmann S (2010) Link communities reveal multiscale complexity in networks. Nature 466(7307):761–764CrossRefGoogle Scholar
 Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 406:378CrossRefGoogle Scholar
 Bak P, Tang C, Wiesenfeld K (1987) Selforganized criticality: an explanation of 1/f noise. Phys Rev Lett 59(4):381–384. MathSciNet
 Barabási AL, 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
 Clauset A, Moore C, Newman MEJ (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453:98CrossRefGoogle Scholar
 de Solla PD (1976) A general theory of bibliometric and other cumulative advantage processes. J Am Soc Inf Sci 27:292CrossRefGoogle Scholar
 Kleinberg J (1999) Authoritative sources in a hyperlinked environment. J ACM 46:604. MATH MathSciNet
 Maslov S, Sneppen K (2002) Specificity and stability in topology of protein networks. Science 296:910CrossRefGoogle Scholar
 Milgram S (1967) The small world problem. Psychol Today 2:60Google Scholar
 Milo R, ShenOrr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824CrossRefGoogle Scholar
 Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89:208701CrossRefGoogle Scholar
 Newman M (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69:066133CrossRefGoogle Scholar
 Newman M, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113CrossRefGoogle Scholar
 PastorSatorras R, Vespignani A (2001) Epidemic spreading in scalefree networks. Phys Rev Lett 86(14):3200–3203CrossRefGoogle Scholar
 Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabási AL (2002) Hierarchical organization of modularity in metabolic networks. Science 297:1551–1555CrossRefGoogle Scholar
 Simon HA (1955) On a class of skew distribution functions. Biometrika 42:425. MATH MathSciNet
 Watts DJ (1999) Small worlds. Princeton University Press, PrincetonGoogle Scholar
 Watts DJ, Strogatz SH (1998) Collective dynamics of “smallworld” networks. Nature 393:440CrossRefGoogle Scholar