Add KADABRA betweenness centrality approximation algorithm

[DerSchmachtin]

Description

This Pull Request introduces the KADABRA (K-ADaptive Approximation of Betweenness centRAlity) algorithm to Graphs.jl.

Computing exact betweenness centrality can be prohibitively expensive on very large graphs. KADABRA provides a fast and highly scalable randomized approximation of the betweenness centrality, as well as an efficient method to find the top-k nodes with the highest betweenness.

The implementation includes two main exported functions:

• kadabra_centrality: Approximates the betweenness centrality for all vertices.
• kadabra_top_k: Returns the top k vertices with the highest betweenness centrality.

Reference:

Borassi M., Natale E. (2016) KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation. In: ESA 2016. [https://dl.acm.org/doi/10.1145/3284359]

A note on the top-k allocation

In top-k mode KADABRA sizes each vertex's confidence interval from its rank gaps before sampling begins. Here the implementation follows the paper (Section 5.2) rather than the authors' C++ reference, which NetworKit's KadabraBetweenness also copies — so a reviewer comparing against either will find a deliberate difference rather than a porting bug:

• The reference pairs the two rank gaps opposite to the way its own stopping test consults them, and leaves lambda_L(v_1) unconstrained — pinning the top vertex's lower budget, the only one its own test uses, at the minimum.
• Its tie-collapse rule is never applied to the pair (v_k, v_{k+1}), the single pair the external-exclusion test is built around, which deadlocks both vertices once their gap falls below 2*err.

The allocation is a heuristic for where to spend the delta budget, not part of the (err, delta) guarantee, so each variant remains a valid approximation and they differ only in how many samples they need. Measured over 4 SNAP graphs × k ∈ {3, 5, 10, 100} × 3 seeds at err = 1e-4, the paper's allocation needed 0.80 ± 0.18 times as many samples as the reference's, at identical top-k accuracy — the same overlap with the exact ranking and the same Kendall τ over the top k to three decimals. Collapsing the boundary pair additionally removes the cases where a top-k query cost more than computing every centrality. See the number of samples in comparison to 'k=0' below. k = 0 is unaffected: it does not enter this code path.

I am separately seeking confirmation from the KADABRA authors on whether the reference's ordering was deliberate (I'm pretty sure it was overlooked), and will report back here. In the meantime I am happy to switch to the reference's behaviour instead if you would prefer bug-for-bug compatibility with NetworKit.

Checklist

• Added kadabra.jl to src/centrality/
• Added corresponding test suite in test/centrality/kadabra.jl and registered it in runtests.jl
• Code has been formatted using JuliaFormatter.jl according to BlueStyle
• Added documentation strings and exported the functions in Graphs.jl
• Ensured RNG scoping follows Graphs.jl conventions using standard library imports

All tests pass locally. Let me know if there are any changes or further optimizations you would like me to make!

Benchmarks & Performance

To verify the performance, I ran some benchmarks comparing this Julia implementation against the original, highly optimized C++ version from the authors.

Hardware Setup:
All benchmarks were executed on an AMD Ryzen Threadripper 3960X 24-Core Processor (3.80 GHz, 48 threads) with 125 GiB of RAM running Ubuntu 22.04 LTS.

The Julia implementation is competitive compared to the Original C++ Implementation.
Here are the results (using k=0, delta=0.1 and epsilon=0.0001) on a few test instances taken from SNAP:

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.62%. Comparing base (356aa72) to head (f5d137c).

Additional details and impacted files

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+ Coverage   97.46%   97.62%   +0.16%     
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  Files         127      129       +2     
  Lines        7766     8340     +574     
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+ Hits         7569     8142     +573     
- Misses        197      198       +1     

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[LoveLow-Global]

Hi there, sorry for the delay in responding. I was very busy thoughout the last couple of weeks, and haven't had the time to look into the new PRs. I will try to review this within a week. Thank you!!