The issue is ERROR 2002 (HY000): Can’t connect to local MySQL server through socket ‘/var/lib/mysql/mysql.sock’ (2 “No such file or directory”) error . This type of error occurred on AlmaLinux / Rocky Linux / Amazon Linux the fix provides the solve this errors.

Pre Steps after occurring the MariaDB installations

Step-I (Install the MariaDB)

On AlmaLinux / Rocky Linux / Amazon Linux 

# yum install mariadb mariadb-server
Step-II (Running MySQL Command)

Firstly Check the mysql command for testing purpose. 

# mysql
 ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2 "No such file or directory")
Step-III (Checking the Mariadb Service)

After that check the mariadb services 

# systemctl status mariadb
 ● mariadb.service - MariaDB 10.0 database server
 Loaded: loaded (/usr/lib/systemd/system/mariadb.service; disabled; vendor preset: disabled)
 Active: inactive (dead)

How to fix this?

Step-I (Start the Mariadb service)

then start the mariadb services. 

# systemctl start mariadb
Step-II (Auto enable the Service)

Finally Service started automatically.  Add the service as systemd system and service managers are on. 

# systemctl enable mariadb
 Created symlink from /etc/systemd/system/multi-user.target.wants/mariadb.service to /usr/lib/systemd/system/mariadb.service.
Step-III (Verify services are stared or not)
# systemctl status mariadb
● mariadb.service - MariaDB 10.0 database server
Loaded: loaded (/usr/lib/systemd/system/mariadb.service; disabled; vendor preset: disabled)
Active: active (running) since Wed 2015-08-19 21:46:13 IST; 8s ago
Process: 18042 ExecStartPost=/usr/libexec/mysql-check-upgrade (code=exited, status=0/SUCCESS)
Process: 17903 ExecStartPost=/usr/libexec/mysql-wait-ready $MAINPID (code=exited, status=0/SUCCESS)
Process: 17710 ExecStartPre=/usr/libexec/mysql-prepare-db-dir %n (code=exited, status=0/SUCCESS)
Process: 17680 ExecStartPre=/usr/libexec/mysql-check-socket (code=exited, status=0/SUCCESS)
Main PID: 17901 (mysqld_safe)
CGroup: /system.slice/mariadb.service
├─17901 /bin/sh /usr/bin/mysqld_safe --basedir=/usr
└─18012 /usr/libexec/mysqld --basedir=/usr --datadir=/var/lib/mysql --plugin-dir=/usr/lib64/mysql/plugin --log-error=/var/log/mariadb/m...
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: The latest information about MariaDB is available at http://mariadb.org/.
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: You can find additional information about the MySQL part at:
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: http://dev.mysql.com
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: Support MariaDB development by buying support/new features from MariaDB
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: Corporation Ab. You can contact us about this at sales@mariadb.com.
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: Alternatively consider joining our community based development effort:
Aug 19 21:46:12 localhost.localdomain mysql-prepare-db-dir[17710]: http://mariadb.com/kb/en/contributing-to-the-mariadb-project/
Aug 19 21:46:12 localhost.localdomain mysqld_safe[17901]: 150819 21:46:12 mysqld_safe Logging to '/var/log/mariadb/mariadb.log'.
Aug 19 21:46:12 localhost.localdomain mysqld_safe[17901]: 150819 21:46:12 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
Aug 19 21:46:13 localhost.localdomain systemd[1]: Started MariaDB 10.0 database server.

Congratulations now you have fixed the cannot connect to local MySQL server through socket error on AlmaLinux / Rocky Linux / Amazon Linux.