Transactions – How many nodes and edges are in the UTXO-coinbase graph?

Imagine a graph where the leaf nodes are UTxO, the middle nodes are consumed as TxO(vout), the root node is the block header and Coinbase Merkle pair, and the edges are the data needed to confirm transitions (e.g. transactions) between nodes. .

Block 831276 How many nodes and edges are currently in this graph? What is the longest path in the graph? Are there any interesting ways to classify graphs in graph theory? For example, is it acyclic? How many disjoint subgraphs are there?

What is the mean/median/range number of leaf-to-root hops through the graph?

Small example subgraph:

root node Blockheader Coinbase-merklepair

Edge0 coinbase

middle node Vout ID of edge0 transaction

Edge 1 *Transaction data support for Edge0 and IntermediateNode*

leaf node vout for unused output from edge1

Thanks to RedGrittyBrick for asking for clarification.