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Cначала определю классы

Point
{
public double X;
public double Y;
}

Node
{
public Point Point;
public double PathLength;
public List<Node> connections;
}

Теперь алгоритм:

foreach(var node in allNodes)
{
    var shape = FindCycleFromNode(node);
}

List<Node> FindCycleFromNode(Node targetNode)
{
    List<Node> openList = new ...
    List<Node> closedList = new ...

    closedList.Add(targetNode);

    Node currentNode = targetNode;

    do
    {
        foreach(var connectedNode in currentNode.Connections)
        {
            if(closedList.Contains(connectedNode) continue;

            if(openList.Contains(connectedNode)
            {
                if(connectedNode.PathLength > currentNode.PathLength + Distance(currentNode.Point, connectedNode.Point))
                {
                    connectedNode.PathLength = currentNode.PathLength + Distance(currentNode.Point, connectedNode.Point);
                }
                else if(Distance(connectedNode.Point, targetNode.Point) == connectedNode.PathLength)//Если значение ноды равно длине до целевой точки.
                {
                    connectedNode.PathLength = currentNode.PathLength + Distance(currentNode.Point, connectedNode.Point);
                }
            }
            else
            {
                connectedNode.PathLength = currentNode.PathLength + Distance(currentNode.Point, connectedNode.Point);
                openList.Add(connectedNode);
            }
        }

        closedList.Add(currentNode);
        openList.Remove(currentNode);

        var nextNode = FindNodeInOpenListWithMinLength(openList);
        currentNode = nextNode;

    }while(openList.Count > 0);

    Node pathNode = null;
    foreach(var node in targetNode.Connections)
    {
        if(node.PathLength > Disntance(node.Point, targetNode.Point))
        {
            if(pathNode == null) pathNode = node;
            else if(pathNode.Length > node.PathLength) pathNode = node;
        }
    }

    List<Node> path = new ...
    path.Add(pathNode);
    while(pathNode != null)
    {
        var nextPathNode = FindMinNode(pathNode.Connections);
        if(nextPathNode == targetNode)
        {
            path.Add(nextPathNode);
            pathNode = null;
        }
        else
        {
            path.Add(nextPathNode);
            pathNode = nextPathNode;
        }
    }

    return path;
}