I am a relatively newbie to GIT and having issues understanding Commit Log graph.
I am under the feeling that each parallel line is a branch.While my source has only 2 branches..I see 3-4 parallel lines in the commit log graph provided below(Microsoft Team Services).Can someone help me understanding this?

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Those connections aren't branches, just references to one or more parent commits. Branches are just pointers/labels to specific commit references. – evolutionxbox Dec 05 '17 at 14:47
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Tags are pointers to specific commits, a branch _name_ describes commit which is currently the _end_ of the branch. – scrutari Dec 05 '17 at 18:57
2 Answers
Correct. Each parallel line is a branch.
In the example image that you gave above those 7-character strings are (short versions of) commit IDs.
For ease of explaining I am going to include this graph (below) that I found online; particularly because it shows the order of the commits, the first commit, and the last commit.
Listing of the branches
In this graph there are four branches. They are:
master branch
(represented by the purple dots)next branch
(represented by the green dots)feature-1 branch
(represented by the pink dots)and
feature-2 branch
(represented by the orange dots)
The line between commit ID 1b43a59 and commit ID 2b59872, and including commit ID 5f357ab and commit ID 3c5bf63, is the master branch
.
The line between commit ID 1b43a59 and commit ID 1ce9df1, and including commit ID dff00dd, is the next branch
.
The line between commit ID 1b43a59 and commit ID 5f357ab, and including commit ID 9ffab9f and commit ID 9db9694, is the feature-1 branch
.
The line between commit ID 1b43a59 and commit ID 3c5bf63, and including commit ID 54a16ed and commit ID 813c45b, is the feature-2 branch
.
Listing of the merges
The feature-1 branch
is merged into the next branch
at the commit represented by commit ID dff00dd.
The feature-1 branch
is merged into the master branch
at the commit represented by commit ID 5f357ab.
The feature-2 branch
is merged into the master branch
at the commit represented by commit ID 3c5bf63.
The feature-2 branch
is merged into the next branch
at the commit represented by commit ID 1ce9df1.
The next branch
is not merged into anything.

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In git, branches are names of so called "heads" – they are related to the top most commits (which – in a simple case – do not have any further, or child, commits). In your case currently you have one branch, but previously there were 4 branches (at the moment of 4e31eddd
), then 3 branches (d9effc23
), and so on until it became one branch at 09d65a15
.
However, even if a branch is merged into another branch it can still be a "head".

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Is there a command where I can get to know the name of those branches.? – raj'sCubicle Dec 04 '17 at 19:49
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A `git branch -a` shows you all current branches both existing locally and remotely. – scrutari Dec 05 '17 at 08:10
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Yes, more precisely: branch names are pointers to branches ends or "heads". More details can be found: https://stackoverflow.com/questions/8196544/what-are-the-git-concepts-of-head-master-origin and https://stackoverflow.com/questions/4386959/difference-between-head-and-master. – scrutari Dec 05 '17 at 18:58