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The phrase "a network that involved" is correct and usable in written English.
It can be used when describing a network that includes or engages certain elements, people, or activities.
Example: "The research focused on a network that involved various stakeholders from different sectors to address climate change."
Alternatives: "a network that included" or "a network that engaged".
Exact(1)
It had been lent to him, he said, by Ptashne, through a network that involved someone's brother-in-law.
Similar(59)
Although packet categorization can be implemented differently in each router, it is important for the provision of services within a network that involves a common understanding of the service level applied to the packets within a flow.
Osteocytes are interconnected by a network that involves their dendritic processes within lacunae to osteoblasts; that mirrors the CNS neuronal network, but comprehensive identity of all relevant signaling molecules in bone remains to be identified [24], [25].
In particular, an ego-network is the part of a network that involves a particular node we are focusing on, which we call ego.
This analysis revealed a self-organizing network that involved predominantly cell to cell contact and movement.
In addition, erbB2 is thought to participate in an important pathway for growth, repair, and survival of adult cardiomyocytes as part of a signaling network that involves neuregulins and the neuregulin receptor erbB4.
We present evidence for a signaling network that involves phosphorylation and reduction of Bcl-xL by IKKβ, and subsequent activation of caspases, which can cleave Htt.
The biofilm formation in Salmonella is tightly regulated by a regulatory network that involves multiple transcriptional regulators.
Furthermore, we show that good fitting conjunction-task connectivity models (Fig. 7A C) require a frontoparietal network that involves both or either of the dorsal and ventral PFC regions.
It would be interesting to see how their results generalize to a contact network that involves more than one group and in which all interactions are recorded.
In B. subtilis 168, there are six proteins (SunI, SunA, SunT, BdbA, SunS, and BdbB) [ 2] taking part in biosynthesizing mature sublancin 168, and the biosynthesis of sublancin 168 is controlled under a complex regulatory network that involves a minimum of five transcriptional regulators, including Abh, AbrB, Rok, YvrG, and YvrH [ 19– 219.
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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