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Properties of Real-World Networks

Real-world networks share common characteristics. When designing network models, we aim to devise models that can accurately describe these 80 P1: WQS Trim: 6.125in × 9.25in Top: 0.5in Gutter: 0.75in CUUS2079-04 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 16:54 4.1 Properties of Real-World Networks 81 networks by mimicking these common characteristics.

To determine these characteristics, one a regular practice is to identify their attributes and show that measurements for these attributes are consistent across networks. In particular, three network attributes exhibit consistent measurements across real-world networks: degree distribution, clustering coefficient, and average path length.

As we recall, degree distribution denotes how node degrees are distributed across a network. The clustering coefficient measures transitivity in a network. Finally, average path length denotes the average distance (shortest path length) between pairs of nodes. We discuss how these three attributes behave in real-world networks next. 4.1.1 Degree Distribution Consider the distribution of wealth among individuals.

Most individuals have an average amount of capital, whereas a few are considered wealthy. In fact, we observe exponentially more individuals with an average amount of capital than wealthier ones. Similarly, consider the population of cities. A few metropolitan areas are densely populated, whereas other cities have an average population size. In social media, we observe the same phenomenon regularly when measuring popularity or interestingness for entities.

For instance, many sites are visited less than a thousand times a month, whereas a few are visited more than a million times daily. Most social media users are active on a few sites, whereas some individuals are active on hundreds of sites.

There are exponentially more modestly priced products for sale compared to expensive ones. There exist many individuals with a few friends and a handful of users with thousands of friends.

 

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