Connecting adverbs are provided in this article. The words listed here are commonly found along with the verb connecting in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb CONNECTING.
actually, closely
directly, emotionally
finally, merely
physically, really
simply, truly
Hope this word list had the connecting adverb you were looking for. In addition to adverbs used with connecting, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.