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The phrase "adding a new edge to" is correct and usable in written English.
It can be used when describing the enhancement or improvement of something, often in a creative or innovative context.
Example: "The artist's latest work is adding a new edge to contemporary art, pushing boundaries and challenging perceptions."
Alternatives: "introducing a fresh perspective" or "bringing a new dimension to".
Exact(1)
Now cheap oil is adding a new edge to its woes.
Similar(59)
Some experts in the field say moving the auction to Paris will add a new edge to the market.
The discovery of significant reserves of oil in the chilly waters surrounding the islands has added a new edge to the dispute.
For example, as one of the most acknowledged network models, the preferential attachment model uses the CND of a node to determine the probability of whether to add a new edge to that node (Barabási and Albert 1999).
At each search step, A-CODE adds a new edge to the candidate community.
For two vertices u and v in a multi-graph G, let G+u v denote the multi-graph obtained by adding a new edge uv to G; when u v∈E(G), let G−u v denote the multi-graph obtained by removing uv from G. Let ℤ + denote the set of nonnegative integers, and let Σ be a set of colors, which correspond to chemical elements such as H, O and C. Let each color c∈Σ be associated with a valence val ( c ) ∈ ℤ +.
One can further augment G' to a size- k' + 1) size- kh G″ by adding a new edge e j to E'.
We form G' by adding a new edge, Ee+1that goes from to.
This section describes a procedure for generating all children G=T+e of a given multi-tree T by adding a new edge e.
If (G_{2}) is obtained from (G_{1}) by deleting the edge (e_{2}) and adding a new edge (e'_{2}=u_{2}v_{2}), we say that (G_{2}) is obtained from (G_{1}) by Operation I, as shown in Figure 2.
In the new model, each time (1) two unconnected nodes are randomly selected, and (2) the probability of adding a new edge between them depends on the difference in their activity states.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com