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We study the algebraic connectivity for several classes of randomsemi-regular graphs. For large random semi-regular bipartite graphs, weexplicitly compute both their algebraic connectivity and as well as the fullspectrum distribution. For an integer $d\in\left[ 3,7\right] $, we findfamilies of random semi-regular graphs that have higher algebraic connectivitythan a random $d$-regular graphs with the same number of vertices and edges. Onthe other hand, we show that regular graphs beat semi-regular graphs when$d\geq8.$ More generally, we study random semi-regular graphs whose averagedegree is $d$, not necessary an integer. This provides a natural generalizationof a $d$-regular graph in the case of a non-integer $d.$ We characterise theiralgebraic connectivity in terms of a root of a certain 6th-degree polynomial.Finally, we construct a small-world-type network of average degree 2.5 with arelatively high algebraic connectivity. We also propose some related openproblems and conjectures.

It is better to be semi-regular when you have a low degree