The eccentricity of a node is the greatest geodesic distance (shortest path) between the node and all the remaining nodes in the network. In BeGraph we calculate it as the greatest geodesic distance between the node and all its reachable nodes in the network. Geodesic distances may be calculated with a link weight that may represent a real distance or cost.
Input parameter  Type  Default  Description 

Distance  text  None  Link property acting as weight for the distance calculations. Must be positive numbers. 
As undirected  Bool  False  Whether to consider a directed network as undirected. It substantially speeds up the execution. 
Calculate eccentricity per connected component  Bool  True  Whether to restrict the distance calculation to reachable nodes, avoiding divergences because formally a node that can not be reached from another node would have infinite eccentricity. 
In the following figure we show two networks. On the left hand side we plot a book characters network we color the nodes according to their eccentricity. The minimum value (3) corresponds to the green node, meaning that any other node is at most three hops away from it. Nodes colored in blue, pink and red have higher eccentricity (4, 5 and 6 respectively) and are not so well connected with the whole network.
The network on the right also shows this quantity on the color nodes, red means high eccentricity (equal to 10) and purple corresponds to the lowest (6).


References