# check whether the given graph is connected
function is_connected(graph::DAG)
    nodeQueue = Deque{Node}()
    push!(nodeQueue, get_exit_node(graph))
    seenNodes = Set{Node}()

    while !isempty(nodeQueue)
        current = pop!(nodeQueue)
        push!(seenNodes, current)

        for child in current.children
            push!(nodeQueue, child)
        end
    end

    return length(seenNodes) == length(graph.nodes)
end

function is_valid(graph::DAG)
    for node in graph.nodes
        @assert is_valid(graph, node)
    end

    for op in graph.operationsToApply
        @assert is_valid(graph, op)
    end

    for nr in graph.possibleOperations.nodeReductions
        @assert is_valid(graph, nr)
    end
    for ns in graph.possibleOperations.nodeSplits
        @assert is_valid(graph, ns)
    end
    for nf in graph.possibleOperations.nodeFusions
        @assert is_valid(graph, nf)
    end

    for node in graph.dirtyNodes
        @assert node in graph "Dirty Node is not part of the graph!"
        @assert ismissing(node.nodeReduction) "Dirty Node has a NodeReduction!"
        @assert ismissing(node.nodeSplit) "Dirty Node has a NodeSplit!"
        if (typeof(node) <: DataTaskNode)
            @assert ismissing(node.nodeFusion) "Dirty DataTaskNode has a Node Fusion!"
        elseif (typeof(node) <: ComputeTaskNode)
            @assert isempty(node.nodeFusions) "Dirty ComputeTaskNode has Node Fusions!"
        end
    end

    @assert is_connected(graph) "Graph is not connected!"

    return true
end