The results offer methods for identifying types of structurally significant people in on-line applications, and suggest a potential expansion of existing theories of tie strength.

7. 𝐺 𝑢
𝐺 𝑢 𝐶 𝑢𝑣
𝐶 𝑢𝑣
𝑑𝑖𝑠𝑝 𝑢, 𝑣 = 𝑑 𝑣(𝑠, 𝑡)
𝑠,𝑡∈𝐶 𝑢𝑣
𝑑 𝑣 𝐶 𝑢𝑣
𝑑 𝑣(𝑠, 𝑡) =
1, 𝑠 𝑒 𝑡 𝑛𝑜𝑛 𝑠𝑜𝑛𝑜 𝑑𝑖𝑟𝑒𝑡𝑡𝑎𝑚𝑒𝑛𝑡𝑒 𝑐𝑜𝑙𝑙𝑒𝑔𝑎𝑡𝑖
𝑒 𝑛𝑜𝑛 ℎ𝑎𝑛𝑛𝑜 𝑣𝑖𝑐𝑖𝑛𝑖 𝑖𝑛 𝑐𝑜𝑚𝑢𝑛𝑒 𝑖𝑛 𝐺 𝑢 𝑜𝑙𝑡𝑟𝑒 𝑎𝑑 𝑢 𝑒 𝑣
0, 𝑎𝑙𝑡𝑟𝑖𝑚𝑒𝑛𝑡𝑖

8. 𝑑𝑖𝑠𝑝 𝑢, 𝑣 𝑒𝑚𝑏 𝑢, 𝑣
𝑑𝑖𝑠𝑝 𝑢, 𝑣
𝑒𝑚𝑏 𝑢, 𝑣
•
𝑛𝑜𝑟𝑚 𝑢, 𝑣 = 𝑑𝑖𝑠𝑝 𝑢, 𝑣 𝑒𝑚𝑏 𝑢, 𝑣
• 𝑛𝑜𝑟𝑚 𝑢, 𝑣

9. 𝑑𝑖𝑠𝑝 𝑢, 𝑣 + 𝑏 𝛼
𝑒𝑚𝑏 𝑢, 𝑣 + 𝑐
𝛼 = 0.61, 𝑏 = 0, 𝑐 = 5
𝐶 𝑢𝑣
𝑥 𝑣 = 1
𝑥 𝑣
𝑥 𝑣 =
𝑥 𝑤
2
+ 2 𝑑 𝑣(𝑠, 𝑡)𝑥 𝑠𝑠,𝑡∈𝐶 𝑢𝑣
𝑥 𝑡𝑤∈𝐶 𝑢𝑣
𝑒𝑚𝑏(𝑢, 𝑣)
𝑥 𝑣
𝑟𝑒𝑐(𝑢, 𝑣)

11. •

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