so as you mentioned I changed code

        List<DiagramNode> FindOverlaps(DiagramNode modifiedNode, Rect bounds, double minDist)
        {

            bounds.Inflate(minDist - 1, minDist - 1);

            var overlaps = new List<DiagramNode>();
            foreach (var node in flowchart.Nodes)
            {
                if (modifiedNode == node)
                    continue;
                if (bounds.IntersectsWith(node.Bounds))
                    overlaps.Add(node);
            }
            return overlaps;
        } 

and all the arrow key operations changed as follows

            // left arrow handler
            flowchart.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateLeft, (sender, args) =>
                {
                    foreach (var node in flowchart.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Left - 10;

                        if (node != null && node.Bounds.Left - 10 >= flowchart.Bounds.Left && (FindOverlaps(node, rect, 5).Count == 0))
                        {
                            node.Move(node.Bounds.Left - 10, node.Bounds.Top);
                        }

                    }
                }));

            // right arrow handler
            flowchart.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateRight, (sender, args) =>
                {
                    foreach (var node in flowchart.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Left - 10;

                        if (node != null && node.Bounds.Right + 10 <= flowchart.Bounds.Right && (FindOverlaps(node, rect, 5).Count == 0))
                        {
                            node.Move(node.Bounds.Left + 10, node.Bounds.Top);
                        }
                    }
                }));

            // up arrow handler
            flowchart.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateUp, (sender, args) =>
                {
                    foreach (var node in flowchart.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Left - 10;

                        if (node != null && node.Bounds.Top - 10 >= flowchart.Bounds.Top && (FindOverlaps(node, rect, 5).Count == 0))
                        {
                            node.Move(node.Bounds.Left, node.Bounds.Top - 10);
                        }
                    }


                }));

            // down arrow handler
            flowchart.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateDown, (sender, args) =>
                {
                    foreach (var node in flowchart.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Left - 10;

                        if (node != null && node.Bounds.Bottom + 10 <= flowchart.Bounds.Bottom && (FindOverlaps(node, rect, 5).Count == 0))
                        {
                            node.Move(node.Bounds.Left, node.Bounds.Top + 10);
                        }
                    }
                })); 

this is compiling without errors, but in here once move one node over other node (overlap) then its locking each other, by selecting one of that overlapped node I can't move node away using arrow keys

so as you mentioned I'updated code,

then Left Arrow Key and Up Arrow Key started to working properly (which is i can close up to 5 pixels, then those are not overlap)

            // left arrow handler
            diagram.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateLeft, (sender, args) =>
                {
                    foreach (var node in diagram.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Left - 10;

                        if (node != null && node.Bounds.Left - 10 >= diagram.Bounds.Left && (FindOverlaps(node, rect, 2).Count == 0))
                        {
                            node.Move(node.Bounds.Left - 10, node.Bounds.Top);
                        }

                    }
                }));

		   // up arrow handler
            diagram.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateUp, (sender, args) =>
                {

                    foreach (var node in diagram.Selection.Nodes)
                    {

                        var rect = node.Bounds;
                        rect.Y = rect.Top - 10;

                        if (node != null && node.Bounds.Top - 10 >= diagram.Bounds.Top && (FindOverlaps(node, rect, 2).Count == 0))
                        {
                            node.Move(node.Bounds.Left, node.Bounds.Top - 10);
                        }
                    }


                })); 

Left Arrow Key Operation with proper distance


Up Arrow Key Operation with proper distance


but Right arrow key and Bottom Arrow key not working like Left Arrow Key and Up Arrow Key , which is can't close up to 5 pixels they are locating with different spaces

            // right arrow handler
            diagram.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateRight, (sender, args) =>
                {

                    foreach (var node in diagram.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.X = rect.Right + 10;

                        if (node != null && node.Bounds.Right + 10 <= diagram.Bounds.Right && (FindOverlaps(node, rect, 2).Count == 0))
                        {
                            node.Move(node.Bounds.Left + 10, node.Bounds.Top);
                        }
                    }
                }));



            // down arrow handler
            diagram.CommandBindings.Add(
                new CommandBinding(Diagram.NavigateDown, (sender, args) =>
                {

                    foreach (var node in diagram.Selection.Nodes)
                    {
                        var rect = node.Bounds;
                        rect.Y = rect.Bottom + 10;

                        if (node != null && node.Bounds.Bottom + 10 <= diagram.Bounds.Bottom && (FindOverlaps(node, rect, 2).Count == 0))
                        {
                            node.Move(node.Bounds.Left, node.Bounds.Top + 10);
                        }
                    }
                }));  

Bottom Arrow Key Operation with wide distance



Right Arrow Key Operation with wide distance



How can I reduce more spaces in right and down arrow handlers like up and left handlers

It should look like this as you've found, otherwise it didn't match the positions where you are moving the node on next line -

// right
rect.X = rect.Left + 10;

// down
rect.Y = rect.Top + 10;