How to use GitHub API to get a repository's dependents information in GitHub?

I don't think you can get the dependents project using Github API (Rest or Graphql), one way could be to use scraping like the following python script :

import requests
from bs4 import BeautifulSoup

repo = "expressjs/express"
page_num = 3
url = '{}/network/dependents'.format(repo)

for i in range(page_num):
    print("GET " + url)
    r = requests.get(url)
    soup = BeautifulSoup(r.content, "html.parser")

    data = [
            t.find('a', {"data-repository-hovercards-enabled":""}).text,
            t.find('a', {"data-hovercard-type":"repository"}).text
        for t in soup.findAll("div", {"class": "Box-row"})

    paginationContainer = soup.find("div", {"class":"paginate-container"}).find('a')
    if paginationContainer:
        url = paginationContainer["href"]

Try this python script