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# Graph Distance

Shortest Path analysis plays a very important role in network analysis. It allows you to determine how quickly information may move through a social network. It can provide you with path planning for cargo shipments. It can even help you determine a set of products to co-purchase. From the description of Dijkstra’s algorithm, you can see that once we select a source node, we compute the shortest path to all the other nodes in the network. As a result, we can determine how “far” the source node is from all other nodes in the network. If we compute Dijkstra’s algorithm for each node in the network, we could form a metric that represents the “centrality” (or, how close the node is on average to other nodes) of each node. The following subsections show various centrality measures we can leverage by computing Dijkstra’s Shortest Path Algorithm for each node. When you use the Network Analysis Tools to compute Graph Distance, the Betweenness Centrality column will be mapped to color (with color gradient and “Softmax” normalization applied).

#### Closeness Centrality

Closeness Centrality is a metric computed for each node that represents the average path length from the given node to all other nodes. The value will range between 0 and 1. A value of 1 implies that this node was the closest (on average) to all other nodes. Nodes with high closeness centrality will typically be found near the center of the network visualization.

#### Betweenness Centrality

Betweenness Centrality is a metric computed for each node that represents the number of computed shortest paths pass through a given node. The value will range between 0 and 1. If a node has a betweenness centrality of 1, it means that the node lies along more shortest paths through the network than any other node. Nodes with high betweenness centrality frequently fall between communities and form bridges between major components of the network.

#### Eccentricity

Eccentricity is a metric computed for each node that represents, of all the shortest paths computed for a node, the largest distance from that node to any other node. The value is always a positive value above 1. The nodes with large eccentricity values will be positioned along the periphery of the network visualization.