By Alvin K Bettinger; John A Englund

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**Additional info for Algebra and trigonometry**

**Example text**

8 An experimental demonstration of the connectivity avalanche. Edges are added to randomly selected pairs of nodes in a set of 100 nodes (cf. previous ﬁgure). The graph shows the number of nodes in the largest clump of nodes. For this network the critical point occurs when 50 edges have been added. 39 December 16, 2013 22:8 PSP Book - 9in x 6in 40 On Graphs, Networks and Social Groups network and the critical point is value at which the connectivity avalanche occurs [21]. A good example is an epidemic.

A graph in which the edges have direction is called a directed graph. A network is simply a graph in which the nodes and/or edges have values associated with them. A family tree, for instance, is a network in which the nodes are people with names, and the edges are family relationships, such as “A is parent of B”. In reality, there are attributes associated with the nodes or edges in virtually any graph. For this reason, we will use the terms “graph” and “network” interchangeably throughout this chapter, except where we are talking about properties of graphs speciﬁcally.

They typically appear when a network consists chieﬂy of “local” connections, but also contains a smattering of “local-range” connections (Fig. 6). Social networks are typically small worlds [12, 13]. In a business, for example, everyone knows the people they work with every day, but they also have some more distant associates, in other organizations. These long-range connections reduce the overall diameter of the network. Strictly speaking, the concept of small world is a property that graphs possess to a greater or lesser degree.

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