added girth

src/GraphInvariants.jl

@@ -28,6 +28,7 @@ struct AverageDegree <: AbstractCardinality end
 
 struct Radius <: AbstractCardinality end
 struct Diameter <: AbstractCardinality end
+struct Girth <: AbstractCardinality end
 
 ##################### Graph Optimal Sets and Cardinalities ##############################
 
@@ -118,6 +119,7 @@ export GraphRule
 
 export Order
 export Size
+export Girth
 
 export MaximumDegree
 export MinimumDegree

src/basics/from_graphs.jl

@@ -88,4 +88,36 @@ function compute(
     g::AbstractGraph{T}
 ) where T <: Integer
     return radius(g)
+end
+
+function compute(
+    ::Type{Girth},
+    g::AbstractGraph{T},
+) where T <: Integer
+
+    shortest_cycle = Inf
+
+    for v in vertices(g)
+        dist = fill(Inf, nv(g))
+        parent = zeros(Int, nv(g))
+        dist[v] = 0
+        q = [v]
+
+        while !isempty(q)
+            current = popfirst!(q)
+            for neighbor in neighbors(g, current)
+                if dist[neighbor] == Inf
+                    push!(q, neighbor)
+                    dist[neighbor] = dist[current] + 1
+                    parent[neighbor] = current
+                elseif parent[current] != neighbor
+                    # We've found a cycle
+                    cycle_length = dist[current] + dist[neighbor] + 1
+                    shortest_cycle = min(shortest_cycle, cycle_length)
+                end
+            end
+        end
+    end
+
+    return isinf(shortest_cycle) ? 0 : shortest_cycle
 end