A final set of computational approaches for networks takes advanced randomness for the analysis. These methods illustrate how thinking through networks may require unconventional perspectives, especially for social scientists. At the same time, these approaches illustrate the benefits of computational analysis compared with traditional descriptive tools.
A random walk is a method to examine the structures and their properties in the network. The random walk starts from a random node in the network and develops a path between that random node and another node within a specified distance (see Example 4.3). We choose randomly one tie of that node and move to the connected node. Therefore, we establish a path between these nodes. We repeat the process from the connected node, i.e. choose a random tie to move forward, until the desired path distance is reached.
The random walk approach can be used to analyse the nodes and their attributes in this random path. Usually, we are not interested in a single random walk but rather repeat them several times. The random walk approach allows us to describe the network and its structure. Unlike traditional descriptive approaches, this approach works in large-scale networks but can also be adapted to various social science questions and theories. For example, Garimella et al. (2016) measure polarisation in a network by examining if a random walk returned to the same community it originated with or not. In the United States, this would mean that if we start from a democrat in the social network, we are interested in if the random walk ends with a democrat or a republican.
All methods discussed above are limited as they describe or quantify a single network. However, they cannot answer the question of how unique the network is with its attributes. To illustrate, if we see a person who is 215 cm tall, is that a high number or a low number for height? Similarly, if our network has a mean degree of five, is that a high degree or a low degree? To allow us to make such an analysis, we must be able to conduct comparisons. However, the challenge with networks is that there is not enough network data to allow us to draw such conclusions. Instead, we use techniques that allow us to generate these comparison points, in a similar fashion to how advanced statistics may use bootstrapping to examine distributions.
The second utilisation of randomness for network analysis is exponential random graph models. We are interested in understanding how the network is built and what causes ties between nodes. The approach is similar to regression models; however, we are unable to use them directly to predict if a tie exists between two nodes. The network structure makes the data points dependable, thus violating some of the assumptions. Rather, computationally, several similar kinds of networks are created based on the data. Then the real network is compared with these random networks. Based on this process, we can make inferences on the types of ties that exist in the network.