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2136 sats \ 0 replies \ @nym OP 23 Nov 2023 \ parent \ on: New metric proposal: Channel Influence Efficiency (CIE) in the Lightning Network bitcoin
Great question!

Network Connectivity (NC) Calculation Formula

NC = λ × (L × U × Q × C × R × N)
Where:
  • NC = Network Connectivity.
  • λ = Normalization factor to scale the result within a meaningful range.
  • L = Liquidity Score, representing the total liquidity available in the node's channels.
  • U = Uptime Score, reflecting the reliability of the node (e.g., a percentage of time the node is online).
  • Q = Quality of Connections Score, indicating the strategic importance of the node's connections (e.g., connections to key nodes).
  • C = Channel Capacity Score, measuring the total capacity of the node's channels.
  • R = Routing Efficiency Score, denoting the node's efficiency in routing transactions (considering factors like latency and path optimality).
  • N = Network Centrality Score, indicating the node's centrality within the network structure.
Utilizing the data from 1ML's Lightning Network statistics, we can calculate an example of network connectivity for a hypothetical node using the proposed formula. For simplicity, we'll assume each factor (liquidity score, uptime score, etc.) is represented on a scale of 0 to 1.
Given Data from 1ML:
  • Network Capacity: 5,368.61 BTC
  • Average Node Capacity: 0.367 BTC
  • Average Channel Capacity: 0.086 BTC
  • Average Node Age: 830.8 days
  • Average Channel Age: 454.8 days
  • Average Channels per Node: 8.52
  • Tor Onion Service Nodes: 10,550 nodes
  • Median Base Fee: 0.632160 sat
  • Median Fee Rate: 0.000050 sat/sat

Example Calculations

Hypothetical Node 1 Data:

  • Liquidity Score (L): Assuming our node's capacity is at 75th percentile, L = 0.75.
  • Uptime Score (U): Assuming an uptime of 95%, U = 0.95.
  • Quality of Connections Score (Q): If our node is connected to key nodes, Q = 0.8.
  • Channel Capacity Score (C): Assuming channel capacity at 75th percentile, C = 0.75.
  • Routing Efficiency Score (R): Assuming high routing efficiency, R = 0.9.
  • Network Centrality Score (N): If the node is moderately central, N = 0.6.

Network Connectivity (NC) Calculation:

Assuming a normalization factor λ = 1, the NC for our hypothetical node would be: NC = 1 × (0.75 × 0.95 × 0.8 × 0.75 × 0.9 × 0.6) NC = 0.22815
This calculated value (0.22815) represents the node's overall connectivity in the network, taking into account various factors like liquidity, uptime, and efficiency. A higher value would indicate a more influential and well-connected node in the network.
For another example, let's calculate the network connectivity for a different type of node in the Lightning Network, perhaps one that is newer or less central:

Hypothetical Node 2 Data:

  • Liquidity Score (L): For a newer node with lower capacity, L = 0.25.
  • Uptime Score (U): If this node has good reliability, but not perfect: U = 0.85.
  • Quality of Connections Score (Q): With less strategic connections, Q = 0.5.
  • Channel Capacity Score (C): Assuming it's around the 25th percentile: C = 0.25.
  • Routing Efficiency Score (R): For a moderately efficient node: R = 0.7.
  • Network Centrality Score (N): As a less central node: N = 0.4.

Network Connectivity (NC) Calculation:

Using the same normalization factor λ = 1, the NC for this hypothetical node would be: NC = 1 × (0.25 × 0.85 × 0.5 × 0.25 × 0.7 × 0.4) NC = 0.014875
This calculated value (0.014875) indicates a relatively lower overall connectivity for this node, reflective of its newer status, lower capacity, and less central position in the network. This node might focus on improving its strategic connections and increasing its capacity to enhance its role in the network.
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