## Centrality analysis

Centrality gives an estimation on how important a node or edge is for the connectivity or the information flow of the network (Figure 27). It is a useful parameter in signalling networks and it is often used when trying to find drug targets.

Centrality analysis in PPINs usually aims to answer the following question:

Which protein is the most important and why?

Edge centrality can also be analysed, but this is less common and the concepts can easily be translated from the node-based centralities, so we will focus on the latter in this section.

Figure 27 Node centrality represented in a network. Bigger, redder nodes have higher centrality values in this representation.

The definition of ‘central’ varies with the context or purpose of our analysis. Centrality can be measured using different metrics and criteria:

• Degree of the nodes

The degree of the nodes can be used as a rough estimate of centrality. As we saw earlier, nodes with a high degree (hubs) are key in maintaining some characteristics of scale-free networks such as their robustness and the small-world effect. However, this is a local measure since it does not take into account the rest of the network and the importance we give to its value depends strongly on the network's size.

• Global centrality measures

Global centrality measures take into account the whole of the network. They are relative measurements that provide a normalised value that is independent of network size. There are many different types of global centrality measures, each addressing a slightly different definition of centrality. Two of the most widely used global centrality measures are closeness and betweenness centralities, which we will address in more detail in the following sections.

• Other measures of centrality

More complex measures of centrality can be defined depending on the specific method used to calculate it. For example, centralities are often calculated using ‘random walks’ where random nodes are chosen as a starting point and the ‘time’ or ‘speed’ needed to reach other nodes in the network is calculated. This can be combined with the weights assigned to nodes or edges in the graph to influence the centrality calculation derived from other features. This is the method used by the Google PageRank algorithm to assign weight to each webpage (12).

Note that centrality parameters can also be calculated taking the directionality of edges into account which can cause slight changes their definitions. Since we are focusing on PPINs, we will consider edges to be undirected in this section.