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Get Information on Graphs

You can use center, periphery, and distance functions to find information about graphs.

    
Wolfram Language code: g = [image];
Wolfram Language code: text[s_] := Style[s, 12, FontFamily -> "Verdana"]
Wolfram Language code: Row[{g, Grid[{{text["Vertex count: "], ToString[VertexCount[g]]}, {text["Edge count: "], ToString[EdgeCount[g]]}, {text["Weighted: "], ToString[WeightedGraphQ[g]]}, {text["Strongly connected: "], ToString[ConnectedGraphQ[g]]}, {text["Radius: "], ToString[GraphRadius[g]]}, {text["Diameter: "], ToString[GraphDiameter[g]]}, {text["Center: "], ToString[First@GraphCenter[g]]}, {text["Periphery: "], ToString[First@GraphPeriphery[g]]}}, Alignment -> Left]}, Spacer[20]]
You can also use free-form linguistics to get information on a graph:
Petersen graph topological properties