Are there possibly mathematica modules that perform the star-mesh transform, in the context of electrical circuit theory? Given a resistor network/graph as input.
More context:
We start off with a graph $G$ of $n$ nodes and a total of $n(n-1)/2$ undirected edges. To each edge, between nodes $i$ and $j$, a value $f_{ij}$ is assigned, with $f$ a given function $f:i,j\to \mathbb{R}$ [*]. If for a given pair of nodes, their edge value is less than a given threshold (so $f<\delta$) then they are considered as disconnected.
Now with the graph $G$ defined as given above, we want to perform the star-mesh transformation on the graph, until a single edge is left. Question was, whether Mathematica has relevant built-in modules that would be considerably helpful in implementing the star-mesh transformation (which in short, keeps removing nodes and updating the edge set and edge values afterwards [**]).
[*]: Any dummy function may be chosen for the purposes of illustration. For instance, a simple function that takes as input the distance between two nodes as input.
[**]: Additional details: For a generic graph $G,$ sequentially, a node is removed (for instance starting from the node with least neighbours), and upon each removal, additional (edges)weights are introduced as follows: if the removen node (r) has $x$ neighbours, then $x(x-1)/2$ weights between each pair of its neighbours are updated. For each pair $a,b$ of its neighbours there can be only two cases:
$a,b$ were already conneted to one another by an edge with weight $w_0,$ in which case their weight is updated to $w=w_0+w_{ra}w_{rb}/\sum_i w_{ri}$ where the sum goes over all neighbours of $r.$
$a,b$ were not previously connected, in which case an edge is added between them with the weight $w=w_{ra}w_{rb}/\sum_i w_{ri}.$
Graph
then, where the weights represent resistances? $\endgroup$