This company has lots of people who have old school ties with 〇〇 University.
I have realized that people at this company throw their weight around because they are all part of the same old boys network from 〇〇 University.
この場合、次のように言うのはいかがでしょうか？
ーThis company has lots of people who have old school ties with 〇〇 University.
「この会社には〇〇大学の学閥の人たちがたくさんいる。」
old school ties で「学閥」と言うので、old school ties with 〇〇 University で「〇〇大学の学閥」と言えます。
ーI have realized that people at this company throw their weight around because they are all part of the same old boys network from 〇〇 University.
「この会社の人たちはみんな〇〇大学の同じ学閥の人たちで幅を利かせていることに気がついた。」
throw one's weight around で「幅を利かせる」
old boys network from 〇〇 University で「〇〇大学の学閥」とも言えます。
ご参考まで！
カナダ 
