How to upgrade PostgreSQL from 9.5 to 9.6.1 without losing data?

When I tried to run psql, I got

psql: could not connect to server: No such file or directory
    Is the server running locally and accepting
    connections on Unix domain socket "/tmp/.s.PGSQL.5432"?

and when I checked Server.log, I saw:

FATAL: database files are incompatible with server
DETAIL: The data directory was initialized by PostgreSQL version 9.5,
        which is not compatible with this version 9.6.1.

I tried to follow this tutorial (from 9.4 to 9.5) for upgrading 9.6.1, but keep getting this error message

cannot write to log file pg_upgrade_internal.log
Failure, exiting

after running

$ pg_upgrade -v \
> -d /usr/local/var/postgres \
> -D /usr/local/var/postgres9.6.1 \
> -b /usr/local/Cellar/postgresql/9.5/bin/ \
> -B /usr/local/Cellar/postgresql/9.6.1/bin/

Does anyone have any idea what I am missing/doing wrong? Thanks!

System:

• MacOS 10.12.2

• PostgreSQL installed with Homebrew

After 9 months, I updated to PostgreSQL 10 from 9.6.5 with pg_upgrade:

1) Stop postgresql:

brew services stop postgresql

2) Initialize postgresql10 database:

initdb /usr/local/var/postgres10.0 -E utf8

3) Double check the newly created db:

ls /usr/local/Cellar/postgresql/

4) Run pq_upgrade to move data to new database:

pg_upgrade \
  -d /usr/local/var/postgres \
  -D /usr/local/var/postgres10.0 \
  -b /usr/local/Cellar/postgresql/9.6.5/bin/ \
  -B /usr/local/Cellar/postgresql/10.0/bin/ \
  -v

5) Rename old database:

mv /usr/local/var/postgres /usr/local/var/postgres9.6.5

6) Rename new database to postgres:

mv /usr/local/var/postgres10.0 /usr/local/var/postgres

7) Restart postgresql:

brew services start postgresql

StackExchange Database Administrators Q#161129, answer score: 4