Centrality measures help gauge the overall importance of a node. In other words, how connected and how influential is a node within the overall network?
One of the simplest measures of centrality is Degree, which measures the number of connections between a node and all other nodes. For instance if we are considering a street network with intersections as nodes, a nodal Degree of 4 would indicate a typical 4-way intersection. The image above depicts a rendition of the Metropolis street network with a Degree value shown at each intersection and a 4-way intersection highlighted in red (Fleischer, 1941). When we focus on what is happening at one particular node, it is called the ego network (in that we are looking at the network from the perspective of a single node while ignoring all nodes not directly connected, which can be deemed a bit narcissistic). The entire network can be called the complete, whole, or global network. So if we want an overall Degree measure, we can calculate Average Degree, which is the average number of connections for all the nodes within the overall network. When the Average Degree exceeds 1, every node has at least one connection, on average. When the Average Degree approaches log(n), where n equals the number of nodes in the network, every node starts to become accessible from every other node (Neal, 2013). For the Metropolis network, there are 78 nodes with an Average Degree of 3.4.
Analyzing Degree measures for a complete network also entails generating a Degree Distribution, which literally equates to the plotting the frequency of each Degree for all the nodes as shown in the image below for the Metropolis street network. The idea is to try to capture the relative differences in connectivity between the nodes in order to gain a sense of network structure. For instance, every node in a homogenous network would have the exact same number of connections and not much of a distribution. A more centralized network might have one node with a high Degree value and all other nodes with low Degree values.