This is Part 2 of the series Degrees of Separation from IXPs. In Part 1: Spatial Concept of Network Quality, we defined “degrees of separation” (hops) from local nodes to an IXP and why it matters for latency, resilience, bandwidth efficiency, and autonomy. Building on that foundation, this post focuses on practical algorithms and methods that help turn those ideas into actionable network planning.

In other words: if Part 1 introduced the “IXP version of a Kevin Bacon number,” Part 2 is about how we actually compute it (and related structure metrics) at scale.

Reducing the degrees of separation between nodes and IXPs is not just a theoretical challenge—it’s a practical way to improve connectivity for underserved regions, ensure better routing efficiency, and enhance overall network performance.

Key Algorithms and Their Applications

Here are the essential techniques that can help uncover hidden hurdles in network architecture:

1. Shortest Path Algorithms

Algorithms like Dijkstra’s and Bellman-Ford enable us to compute the shortest paths—from nodes to their closest IXPs—using different definitions of “distance”:

  • Hop count (logical degrees of separation)
  • Layer/site transitions (physical separation)
  • Latency/cost/risk weights (experienced separation)

Questions these algorithms can answer include:

  • Which nodes are most isolated from IXPs?
  • How can we reduce the longest paths in the network to enhance efficiency for everyone?

2. Centrality Measures

These metrics allow us to evaluate the importance of nodes within the network structure:

  • Betweenness Centrality: Identifies nodes that act as critical intermediaries or bottlenecks.
  • Closeness Centrality: Highlights well-positioned nodes capable of maintaining low-latency connections to IXPs.

3. Weighted Graph Models

Assigning weights to edges based on bandwidth, latency, or resilience risks enables us to simulate real-world network conditions. Weighted graphs are used to:

  • Uncover hidden inefficiencies in bandwidth utilization.
  • Pinpoint high-latency links for targeted upgrades.

4. Community Detection

Algorithms such as Louvain or Girvan-Newman help identify clusters of nodes that share high proximity to IXPs—or, conversely, poorly connected and underserved communities. Clustering approaches are particularly effective for:

  • Identifying rural areas that could benefit from regional IXPs.
  • Planning geographically equitable infrastructure upgrades.

5. GIS-Integrated Analysis

The integration of graph analysis with geospatial data provides a way to directly visualize regional differences in connectivity. Tools like Voronoi partitioning and spatial autocorrelation can illustrate the geographic divide in network access, pointing out urgent areas for development.

6. Semantic Graph Queries

By applying SPARQL or other reasoning tools, planners can develop sophisticated models to test “what-if” scenarios:

  • For instance, queries like Node_A —[connected_to]→ Node_B and Node_B —[distance_to]→ IXP_C = 3 hops simulate potential benefits of upgrading nodes or links.

Transforming Insights Into Action

So, how do these tools shape the networks of tomorrow? Consider the practical benefits:

  1. Lower Latency: Reduced separation from IXPs allows end users to experience faster response times.
  2. Resilience: Addressing bottlenecks makes networks less vulnerable to localized disruptions.
  3. Bandwidth Efficiency: Improving connections to IXPs alleviates pressure on high-traffic routes.
  4. Equity in Access: By targeting underserved regions, infrastructure development can bridge key connectivity gaps.

A practical measurement stack (townships/cities)

If homes and businesses are the unit of analysis and townships/cities are your smallest regions, a practical workflow is:

  1. Compute a township/city summary for each separation definition: logical hops, physical hops, and weighted distance (e.g., latency-to-nearest-IXP).
  2. Compare places on each metric and flag where the metrics disagree (e.g., low-hop but high-latency paths).
  3. Use the mismatch to guide action: peering/routing changes (logical), facility/middle-mile investments (physical), or congestion/capacity upgrades (weighted).

Making equity measurable (Gini + HĂĄjek)

If your unit of analysis is homes and businesses, and townships/cities are your smallest planning regions, you can use the algorithms above to compute one or more separation metrics per place, then quantify how unevenly those outcomes are distributed.

Credit: I learned the Gini coefficient framing and the HĂĄjek estimator approach for weighted estimation from Dr. Stilian Stoev (University of Michigan Statistics Department).

  • Gini coefficient: Summarizes inequality across townships/cities—useful when the average improves but the worst-off places barely move.
  • HĂĄjek estimator (weighted estimation): Real-world measurements are often uneven (more probes/tests in urban areas). A HĂĄjek-style weighted estimate helps translate sampled measurements into population-relevant estimates by weighting townships/cities by homes + businesses (or another exposure proxy) so results reflect lived experience, not measurement density.

Next Steps

The analysis doesn’t end here. Every node, every connection, and every hop reveals a broader picture of global opportunities—opportunities to optimize, connect, and innovate. Looking ahead, the focus must remain on translating insights into real-world upgrades that empower networks at every scale.

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