Compute eccentricity centralities:

Highlight:

Rank vertices. Highest-ranked vertices are at short distances to every other reachable vertex:

EccentricityCentrality works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

EccentricityCentrality works with large graphs:

Rank vertices by their eccentricity:

Highlight the eccentricity centrality for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

Based on the infrastructure network of the Marshall Islands in eastern Micronesia, find a strategically located island:

It is different with the median of the graph:

A road network linking Chicago suburbs. Find the best location for hospitals and fire departments, to minimize the distance traveled by emergency vehicles:

For graphs with vertices, the largest sum in differences in eccentricity centrality between the most central vertex and all other vertices is the inverse of :

Measure how central the most central vertex is with respect to other vertices:

Centralization of social networks:

EccentricityCentrality is the inverse of maximum distances to other reachable vertices:

The inverse of maximum distances to other reachable vertices:

Eccentricity centrality of a vertex is the reciprocal of the VertexEccentricity:

Eccentricity centrality is between 0 and 1:

Eccentricity centralities for an undirected graph are equivalent to centralities for each component:

Computing the centralities for each component yields the same result:

Use GraphCenter to find vertices with the highest eccentricity centrality:

Use VertexIndex to obtain the centrality for a specific vertex: