This is a partial set of clean-ups. There could be others, but they may be controversial (e.g. adopting LINQ in some areas, which may or may not hurt performance). I've also tried to be mindful of target framework versions and also some edge cases (e.g. hashing) where seemingly redundant chunks of code, if removed or changed for another option, may blow things up.

See what you think.

Pre-change:

// * Summary *

BenchmarkDotNet=v0.12.1, OS=endeavouros
AMD Ryzen 7 5800H with Radeon Graphics, 1 CPU, 16 logical and 8 physical cores
.NET Core SDK=8.0.108
  [Host]     : .NET Core 8.0.8 (CoreCLR 8.0.824.36612, CoreFX 8.0.824.36612), X64 RyuJIT
  Job-GRIUMJ : .NET Core 8.0.8 (CoreCLR 8.0.824.36612, CoreFX 8.0.824.36612), X64 RyuJIT

IterationCount=1  LaunchCount=1  WarmupCount=1

|         Method | EdgeCount |       Mean | Error |     Gen 0 |     Gen 1 |     Gen 2 | Allocated |
|--------------- |---------- |-----------:|------:|----------:|----------:|----------:|----------:|
| Intersection_N |      1000 |   119.9 ms |    NA | 1000.0000 |         - |         - |   9.04 MB |
| Intersection_N |      2000 |   542.1 ms |    NA | 1000.0000 |         - |         - |   16.2 MB |
| Intersection_N |      3000 | 1,431.1 ms |    NA | 5000.0000 | 4000.0000 | 1000.0000 |  37.28 MB |
| Intersection_N |      4000 | 3,008.9 ms |    NA | 6000.0000 | 5000.0000 | 1000.0000 |  47.41 MB |
| Intersection_N |      5000 | 6,173.7 ms |    NA | 9000.0000 | 8000.0000 | 1000.0000 |  74.05 MB |

// * Legends *
  EdgeCount : Value of the 'EdgeCount' parameter
  Mean      : Arithmetic mean of all measurements
  Error     : Half of 99.9% confidence interval
  Gen 0     : GC Generation 0 collects per 1000 operations
  Gen 1     : GC Generation 1 collects per 1000 operations
  Gen 2     : GC Generation 2 collects per 1000 operations
  Allocated : Allocated memory per single operation (managed only, inclusive, 1KB = 1024B)
  1 ms      : 1 Millisecond (0.001 sec)

// * Diagnostic Output - MemoryDiagnoser *

// ***** BenchmarkRunner: End *****
// ** Remained 0 benchmark(s) to run **
Run time: 00:00:47 (47.83 sec), executed benchmarks: 5

Global total time: 00:00:57 (57.28 sec), executed benchmarks: 5

Post-change:

// * Summary *

BenchmarkDotNet=v0.12.1, OS=endeavouros
AMD Ryzen 7 5800H with Radeon Graphics, 1 CPU, 16 logical and 8 physical cores
.NET Core SDK=8.0.108
  [Host]     : .NET Core 8.0.8 (CoreCLR 8.0.824.36612, CoreFX 8.0.824.36612), X64 RyuJIT
  Job-WWTCPL : .NET Core 8.0.8 (CoreCLR 8.0.824.36612, CoreFX 8.0.824.36612), X64 RyuJIT

IterationCount=1  LaunchCount=1  WarmupCount=1

|         Method | EdgeCount |       Mean | Error |     Gen 0 |     Gen 1 |     Gen 2 | Allocated |
|--------------- |---------- |-----------:|------:|----------:|----------:|----------:|----------:|
| Intersection_N |      1000 |   127.1 ms |    NA |         - |         - |         - |   6.85 MB |
| Intersection_N |      2000 |   475.1 ms |    NA | 2000.0000 | 1000.0000 |         - |  23.04 MB |
| Intersection_N |      3000 | 1,408.1 ms |    NA | 5000.0000 | 4000.0000 | 1000.0000 |  36.15 MB |
| Intersection_N |      4000 | 2,874.6 ms |    NA | 5000.0000 | 4000.0000 | 1000.0000 |  41.76 MB |
| Intersection_N |      5000 | 5,954.3 ms |    NA | 9000.0000 | 8000.0000 | 2000.0000 |  68.62 MB |

// * Legends *
  EdgeCount : Value of the 'EdgeCount' parameter
  Mean      : Arithmetic mean of all measurements
  Error     : Half of 99.9% confidence interval
  Gen 0     : GC Generation 0 collects per 1000 operations
  Gen 1     : GC Generation 1 collects per 1000 operations
  Gen 2     : GC Generation 2 collects per 1000 operations
  Allocated : Allocated memory per single operation (managed only, inclusive, 1KB = 1024B)
  1 ms      : 1 Millisecond (0.001 sec)

// * Diagnostic Output - MemoryDiagnoser *

// ***** BenchmarkRunner: End *****
// ** Remained 0 benchmark(s) to run **
Run time: 00:00:46 (46.34 sec), executed benchmarks: 5

Global total time: 00:00:51 (51.28 sec), executed benchmarks: 5