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In this section, we consider a cellular network that consists of one base station (BS) and many user equipments (UEs). We call the BS and all the UEs as the nodes.

I learned that the verb 'call' is used like "I call him a superman." Do I have to delete 'as'?

However, the following sentence looks very awkward.

We call the BS and all the UEs the nodes.

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"Call as" is not idiomatic. Deleting "as" but retaining "the" results in a grammatical construction, but I agree that it sounds a bit awkward. "We call the BS and all the EUs nodes" is more idiomatic. I point out that even the last version is possibly open to misinterpretation. I cannot be positive that what is meant is "We call the BS and each EU a node" or "We call the BS a node and the EUs collectively a node." I am 99% sure that the former is meant, but why not avoid any possibility for misinterpretation.

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I don't think you need to use "as" with "call".

We call her "The Tiger Lady"

"As" is required with a different verb, like "refer to":

We refer to her as "The Tiger Lady".

That being said, your sentence is confusing. Might I suggest:

The BS and all the UEs are collectively called the "nodes" of the network.

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  • I think it's just as good to say The BS and the UEs are called "nodes."
    – Ringo
    Dec 28, 2017 at 17:55
  • I cannot write double quotation marks in my paper. The third one is very nice. Thank you.
    – Danny_Kim
    Dec 28, 2017 at 17:58
  • Can I ask one more thing??? I want to explain the following sets. * A = {(x1,y1), (x2,y2), (x3,y3)} * B = {(x4,y4), (x5,y5), (x6,y6)} * C = {(x7,y7), (x6,y6), (x9,y9)} Which is correct? > (A set / Sets) of (the locations / the location / locations / location) of the rabbits, the lions, and the tigers are denoted by A, B, and C.
    – Danny_Kim
    Dec 28, 2017 at 17:58
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    "The locations of x, y, and z ... are denoted by A, B, and C respectively" avoids any possible confusion. Dec 28, 2017 at 18:02
  • @JeffMorrow Thank you for answer! In my case, I have to mention that they are sets because I am writing a Math paper.
    – Danny_Kim
    Dec 28, 2017 at 18:03

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