Fix error in implementation of Erdos-Gallai condition in isgraphical

Fixes #400

Fix `isgraphical` function to correctly handle non-graphical sequences.

# Error in current implementation

`mindeg` is computed globally at the start using `min(i, sorted_degs[i])` for all indices. However, the Erdös-Gallai condition requires dynamically calculating `min(r, sorted_degs[i])` for vertices after the current index `r`.

# What changed

* Update the Erdös-Gallai condition check to calculate the sum of the minimum of r and the degrees of the vertices.

* Add a test case in `test/connectivity.jl` to verify that `isgraphical` returns false for the sequence [4,2,2,2,0].

---

For more details, open the [Copilot Workspace session](https://copilot-workspace.githubnext.com/JuliaGraphs/Graphs.jl/issues/400?shareId=XXXX-XXXX-XXXX-XXXX).

Author: Syuizen

src/connectivity.jl

@@ -805,17 +805,12 @@ function isgraphical(degs::AbstractVector{<:Integer})
     sorted_degs = sort(degs; rev=true)
     # Compute the length of the degree sequence
     cur_sum = zero(UInt64)
-    # Compute the minimum of each degree and the corresponding index
-    mindeg = Vector{UInt64}(undef, n)
-    @inbounds for i in 1:n
-        mindeg[i] = min(i, sorted_degs[i])
-    end
     # Check if the degree sequence satisfies the Erdös-Gallai condition
-    cum_min = sum(mindeg)
     @inbounds for r in 1:(n - 1)
         cur_sum += sorted_degs[r]
-        cum_min -= mindeg[r]
-        cond = cur_sum <= (r * (r - 1) + cum_min)
+        # Calculate the sum of the minimum of r and the degrees of the vertices
+        mid_deg_sum = sum([min(r, sorted_degs[i]) for i in (r + 1):n])
+        cond = cur_sum <= (r * (r - 1) + mid_deg_sum)
         cond || return false
     end
     return true

test/connectivity.jl

@@ -316,6 +316,7 @@
     @test @inferred(isgraphical([2, 2, 2]))
     @test @inferred(isgraphical(fill(3, 10)))
     @test @inferred(isgraphical(Integer[]))
+    @test @inferred(!isgraphical([4, 2, 2, 2, 0]))
     ##@test !@inferred(isgraphical([2]))
 
     # Test simple digraphicality