This Demonstration shows a family of biregular graphs that arise in the study of inverse problems on electrical networks. The blue nodes are boundaries and the red nodes are interiors. The sliders control the size of the blue clusters, the total number of blue clusters, and the number of clusters incident to any red node.
Each of these graphs is called a "star". There is a transformation that yields an electrically equivalent "K" network. Studying the "K" network allows one to determine recoverability properties of the inverse problem. For more information, see  in the Details section.
Biregular graphs such as these arise in projective geometry due to the Levi graph construction.