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Similarity Measure (I): Geodesic Distance

  • Geodesic distance (A, B): length (i.e., # of edges) of the shortest path between A and B (if not connected, defined as infinite)
  • Eccentricity of v, eccen(v): The largest geodesic distance between v and any other vertex u ∈ V − {v}.
    • E.g., eccen(a) = eccen(b) = 2; eccen(c) = eccen(d) = eccen(e) = 3
  • Radius of graph G: The minimum eccentricity of all vertices, i.e., the distance between the “most central point” and the “farthest border”
    • r = min v∈V eccen(v)
    • E.g., radius (g) = 2
  • Diameter of graph G: The maximum eccentricity of all vertices, i.e., the largest distance between any pair of vertices in G
    • d = max v∈V eccen(v)
    • E.g., diameter (g) = 3
  • A peripheral vertex is a vertex that achieves the diameter.
    • E.g., Vertices c, d, and e are peripheral vertices

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