# Graph having largest algebraic connectivity among some given blocks

Suppose we are given some blocks(in sense of graph theory). Now suppose we have to find out that graph(connected) which has maximum algebraic connectivity and consists of those given blocks. the blocks may be path graph,cycle etc.please explain with a sage code.

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The question / the request is unclear for me. First of all do we have as input a Block graph $G$? ("Some blocks" is not really clarifying the input.)
• among all connected subgraphs $H$ of $G$ which "consist of (some of the) given blocks" (does this mean "for every block $B$ of $G$ if $H$ contains an edge of $B$, then it contains the whole $B$ as a subgraph?!)
• the subgraph(s) $H$ which maximize the algebraic connectivity?!