The inner lines and arrows are sometimes used to represent additional influences or movements between the personality types. The two most common uses are stress/security points and directions of integration/disintegration. The arrows may also be ignored and the lines described as connecting points where a movement away from the dominant type to one of the other types can occur temporarily.
More details about the inner lines can be found in the Enneagram User Guide series book Decoding the Enneagram. This book specifically explores how Gurdjieff used the inner lines and how the personality types use the inner lines and arrows. Check the home page for the latest information about the availability of this book, other books, and related projects.