Elements of Access: Degree

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? DEGREE VALUES FOR METROPOLIS STREET 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. Elements of Access: Transport Planning for Engineers, Transport Engineering for Planners. By David M. Levinson, Wes Marshall, Kay Axhausen.

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.