Create continuous path from multiple segments

[hsharghi]

I have an array of several segments of a path with known start / end point. Direction of each segment is not known. It can be from start to end point or vice versa.
Each segment object is something like this:
Connection: {
PointA = p1
PointB = p2
pointA_is_connected = true (false for the first or last segment)
pointB_is_connected = true (false for the first or last segment)
}

I want to create a path from one end to another in one direction with all segments that can be connected to each other. All the segments in an array are segments of a ONE path.
Here is an image of what I have (in red) and what I want to have (in green)
What's the best way to achieve this?

note.jpg