In NetworkX, the Graph class is used to represent undirected networks and analyze their structure. The previous chapter showed how to create a network from scratch by adding nodes and edges. This section will instead use one of the ready-made networks available in NetworkX: Zachary's karate club (Zachary, 1977).

This network represents the friendships (edges) between members (nodes) of a karate club studied between 1970 and 1972. This particular karate club has long been of interest to sociologists and network scientists, because it eventually split into two different clubs after a disagreement between the instructor and the club president (this might explain why there aren't any famous studies of conflict resolution clubs). In the original study, Zachary used the network structure to predict which members would join which...

In the last chapter, I said that networks were entirely defined by the number of nodes and which nodes were connected. I lied. Kind of. Now that we're all a little older and wiser than we were in Chapter 1, What is a Network?, I can tell you the whole truth: sometimes, network nodes and edges are annotated with additional information. In the Graph class, each node and edge can have a set of attributes to store this additional information. Attributes can simply be a convenient place to store information related to the nodes and edges, or they can be used by visualizations and network algorithms.

The Graph class allows you to add any number of attributes to a node. For a G, network, each node's attributes are stored in the dict at G.nodes[v], where v is the node's ID. In the karate club example, the club members eventually split...

So far, all of the edges in this chapter have been unweighted, but the Graph class also supports weighted edges. Edge weights are handy when connections can have different strengths and when there is a way to quantify the strength of a connection; for example, how often two friends talk to each other, the volume of fluid a pipe can transport, or the number of direct flights between two cities.

The karate club network doesn't have any additional information about the strength of the edges, but there are relevant properties of those edges that can be calculated, such as the tie strength. Tie strength increases with the number of neighbors that two nodes have in common. It is motivated by the observation that closer friends tend to have more friends in common, and it can often reveal insight into the structure of a social network. The following code calculates...

So far, all of the edges in this chapter have been undirected, with no difference between an edge from A to B, and an edge from B to A. But not all relationships in life are so symmetric. If an employee-boss relationship is described by an undirected edge, it suggests that the employee can fire the boss as easily as the other way around. While possibly good for workplace morale, such arrangements aren't the norm. NetworkX supports directed edges through the DiGraph (directed graph) class.

Many of the operations already described for the Graph class translate seamlessly to the DiGraph class. Iterating through nodes and edges, accessing attributes, and visualization are all exactly the same. But there are a few differences. This section will describe the most important of these differences.

This section will use another social...

Meanwhile, in 18th-century Königsberg, both Graph and DiGraph fall short. Several of the bridges of Königsberg (discussed in Chapter 1, What is a Network?) connected the same two landmasses. In order to represent the bridges as a network, the nodes representing the land masses need to have multiple parallel edges, but the Graph class only allows one edge between a pair of nodes. For situations like this, NetworkX provides the MultiGraph and MultiDiGraph classes. For many applications, parallel edges can be combined into a single weighted edge, but when they can't, these classes can be used.

These MultiGraph and MultiDigraph classes work very much like Graph and DiGraph, but allow parallel edges. Any number of edges can be added between the same two endpoints. The following example reconstructs the Königsberg...

All networks are composed of nodes and edges, but different systems require nodes and edges with different attributes. This chapter introduced the Graph class for undirected networks, and the DiGraph class for directed networks, as well as the MultiGraph and MultiDiGraph classes. In addition, this chapter demonstrated how to attach data to nodes and edges using attributes. Now you know how to access the basic properties of a network in NetworkX using these classes, but where do those networks come from? The next chapter describes various techniques for creating networks from data.

The following is a list of resources that you can consider to get further knowledge:

• Zachary, W. W. (1977). An information flow model for conflict and fission in small groups. Journal of anthropological research, 33(4).
• Knecht, A. B. (2008). Friendship selection and friends’ influence (Doctoral dissertation). Utrecht University.