local clustering coefficient

Table of Contents

notation: \(N(v)\) - neighbors of \(v\), \(e(N(v))\) - number of edges between neighbors of \(v\) \[ \text{lc}_v = \frac{e(N(v))}{C_2^{\text{deg}v}} \] Interpretation - Ratio of all the connection between neighbors of node \(v\) and number of all possible links among \(v\)’s neighbors; or the of \(v\)’s neighbors.

If this value is high - \(v\)’s neighbors are connected, \(v\) is not very important If this value is low - \(v\)’s neighbors are not connected, the traffic relies on \(v\)

1. global measure

a global measure with local clustering coefficient is the average local clustering coefficient \[ lv = \frac{1}{n}\sum_V\text{lv}_v \]

  • fully conntected network have \(lc = 1\)

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local clustering coefficient

(global measure)

a global measure with local clustering coefficient is the average local clustering coefficient \[ lv = \frac{1}{n}\sum_V\text{lv}_v \]

  • fully conntected network have \(lc = 1\)

Author: Linfeng He

Created: 2024-04-03 Wed 23:18