Dear Rithesh K,

Concerning Diameter, Radius and eccentricities, there is this very good 
recent paper [1].
It is written for undirected, unweigthed graphs, but the algorithms can be 
easily extended to weighted graphs.
Directed graphs requires more care. See for instance [2] and papers citing 
it
You can also read the PhD thesis of Michele Borassi [3] (former 
GSoC/Sagemath student now at Google Zurich).

David.

[1] Feodor Dragan 
<https://arxiv.org/search/cs?searchtype=author&query=Dragan%2C+F>, Michel 
Habib <https://arxiv.org/search/cs?searchtype=author&query=Habib%2C+M>, Laurent 
Viennot. Revisiting Radius, Diameter, and all Eccentricity Computation in 
Graphs through Certificates. 
<https://arxiv.org/search/cs?searchtype=author&query=Viennot%2C+L>
http://arxiv.org/abs/1803.04660
[2] Takuya Akiba, Yoichi Iwata <https://dblp.org/pers/hd/i/Iwata:Yoichi>, Yuki 
Kawata <https://dblp.org/pers/hd/k/Kawata:Yuki>: An Exact Algorithm for 
Diameters of Large Real Directed Graphs. SEA 2015 
<https://dblp.org/db/conf/wea/sea2015.html#AkibaIK15>: 56-67 
https://doi.org/10.1007/978-3-319-20086-6_5 
<http://dx.doi.org/10.1007/978-3-319-20086-6_5>
[3] Borassi, Michele (2016) *Algorithms for metric properties of large 
real-world networks from theory to practice and back.* Advisor: Crescenzi, 
Prof. Pierluigi. Coadvisor: De Nicola, Prof. Rocco . pp. 262. 
http://e-theses.imtlucca.it/198/


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