What the diagram provides is a map on which different pieces of work can be located. You can see that on Carl's original post. As this is a map within a map you should check out the original first and use this one to zoom in on the particular issues associated with local digital democracy.
Below is a first stab and collecting together some relevant pieces of work. This is very much early days. If you know of any others please let us know.
Overview and Context
The Left Hand Side of the Framework
The Middle Section of the Framework
The Networked Councillor
CllrSocmed: Social Media for Councillors
Social Council Decision Making