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Fundamentals of complex networks : models, structures and dynamics
Chen G., Wang X., Li X., Wiley Publishing, Hoboken, NJ, 2015. 392 pp. Type: Book (978-1-118718-11-7)
Date Reviewed: Aug 9 2016

The term “network,” widely used in many diverse areas ranging from computer science to biology, refers to the interconnection of various entities to facilitate information exchange. The adjective “complex” in “complex networks” is used to capture nontrivial topological features that occur in networks used for modeling real systems. Complex networks are used to model the following few representative problems drawn from various areas. In computer science, they are used to model the number of clicks on the Web and virus propagation on the Internet. In social networking, they are used to model rumor propagation. In biological sciences, they are used to model the propagation of epidemics like AIDS and SARS.

Mathematically, a network is abstracted as a graph that comprises a set of nodes and a set of links. Links are used to connect various network nodes and thereby to capture interdependencies between various nodes. The idea of abstracting a “physical” network as a “mathematical” graph was originated by the great French mathematician Leonhard Euler. Henceforth, we shall use the words network and graph interchangeably. Any graph in general can be characterized in terms of various features like degree (and its associated probability distribution), clustering, and assortativity. For example, the feature (average) degree would help give an idea about the number of incoming and outgoing links that a given node may possess on average. Similarly, feature clustering, measured in terms of clustering coefficient, would help determine the extent of friendship that two nodes in a social network might have. Most computer/social/biological networks that we encounter in real life possess features (like degree, clustering, and assortativity) that are neither purely random nor purely non-random. Indeed some of the simple (noncomplex) networks that have been extensively studied in literature are devoid of such behavior. Therefore, real-life networks can be better handled under the framework of complex networks.

Two well-studied classes of complex networks are scale-free and small-world networks. Scale-free networks (which are heterogeneous in terms of their connectivity) have node-degree distributions in the power-law form and are indeed independent of the connectivity scale, hence the name “scale-free” networks (this is in contrast to the behavior exhibited by networks that are homogeneous in terms of their connectivity). Small-world networks, discovered by Watts and Strogatz in 1998 [1], possess features like large clustering coefficients and short path lengths. This monograph, Fundamentals of complex networks, provides a concise treatment of complex networks that is suitable for students who are starting to study this exciting and rapidly developing area. The authors have made a deliberate attempt to keep this book at a very introductory level and have focused extensively on numerous application areas that occur in various domains. The entire book has been divided into two parts: “Fundamental Theory” (Part 1) and “Applications” (Part 2). Chapter 2 of Part 1 covers the basic concepts of graph theory, while chapter 3 covers basic concepts related to complex networks. Part 2 covers applications from the following diverse areas: computer networks, social networks, and network control.

In conclusion, this monograph provides a basic overview of complex networks and demonstrates how some of the concepts can be applied in diverse areas. However, the book does not provide the type of in-depth coverage on the topic presented in [2]. It can be used as a reference for someone getting started in the ever-evolving field of computer networks.

Reviewer:  Laxminarayana Pillutla Review #: CR144676 (1611-0798)
1) Watts, D. J.; Strogatz, S. H. Collective dynamics of small-world networks. Nature 393, 6(1998), 440–442.
2) Newman, M. Networks: an Introduction. Oxford University Press, Oxford, UK, 2010.
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