Weighted networks

Returning to the case of undirected networks, sometimes, not all edges are created equal. For example, in a network representing a city's water distribution system, the edges could represent a series of tubes that carry the water from one place to another. Some of these might have greater capacity than others. When edges can have different strengths, the network is called weighted, and the strength is quantified by a number called the weight. Both directed and undirected networks can be weighted. An example of a weighted network is shown in the following diagram. When visualizing a network, edge weights are often indicated by varying the thickness or opacity of the edge. Edge weights can be used to represent many different types of attributes. The most common ones are described in the next section: