You will have to run one query per degree of separation.

I'll assume the following schema (SQLite dialect):

CREATE TABLE person (
    id   INTEGER NOT NULL,
    name TEXT,
    PRIMARY KEY ( id )
);
CREATE TABLE friend (
    person INTEGER NOT NULL,
    friend INTEGER NOT NULL,
    PRIMARY KEY ( person, friend )
);
[download]

Then your graph would be

INSERT INTO person VALUES ( 1, 'Al' );
INSERT INTO person VALUES ( 2, 'Bob' );
INSERT INTO person VALUES ( 3, 'Chuck' );
INSERT INTO person VALUES ( 4, 'Doug' );
INSERT INTO person VALUES ( 5, 'Ed' );
INSERT INTO person VALUES ( 6, 'Frank' );
INSERT INTO person VALUES ( 7, 'Gary' );
INSERT INTO person VALUES ( 8, 'Hamza' );
INSERT INTO person VALUES ( 9, 'Ibrahim' );
INSERT INTO friend VALUES ( 1, 2 );
INSERT INTO friend VALUES ( 1, 3 );
INSERT INTO friend VALUES ( 1, 6 );
INSERT INTO friend VALUES ( 1, 9 );
INSERT INTO friend VALUES ( 2, 1 );
INSERT INTO friend VALUES ( 2, 4 );
INSERT INTO friend VALUES ( 2, 7 );
INSERT INTO friend VALUES ( 3, 1 );
INSERT INTO friend VALUES ( 3, 4 );
INSERT INTO friend VALUES ( 3, 5 );
INSERT INTO friend VALUES ( 3, 6 );
INSERT INTO friend VALUES ( 4, 2 );
INSERT INTO friend VALUES ( 4, 3 );
INSERT INTO friend VALUES ( 4, 8 );
INSERT INTO friend VALUES ( 5, 3 );
INSERT INTO friend VALUES ( 6, 1 );
INSERT INTO friend VALUES ( 6, 3 );
INSERT INTO friend VALUES ( 7, 2 );
INSERT INTO friend VALUES ( 7, 8 );
INSERT INTO friend VALUES ( 7, 9 );
INSERT INTO friend VALUES ( 8, 4 );
INSERT INTO friend VALUES ( 8, 7 );
INSERT INTO friend VALUES ( 9, 1 );
INSERT INTO friend VALUES ( 9, 7 );
[download]

With this you can figure out a person's friends by joining the tables:

sqlite> SELECT P1.name, P2.name                              
   ...> FROM person P1 
   ...> JOIN friend F ON P1.id = F.person 
   ...> JOIN person P2 ON F.friend = P2.id 
   ...> WHERE P1.name = 'Bob' ;
P1.name|P2.name
Bob|Al
Bob|Doug
Bob|Gary
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For the friends' friends you use a subselect:

sqlite> SELECT P1.name, P2.name
   ...> FROM person P1
   ...> JOIN friend F ON P1.id = F.person
   ...> JOIN person P2 ON F.friend = P2.id
   ...> WHERE P1.id IN (     
   ...>   SELECT F.friend
   ...>   FROM person P
   ...>   JOIN friend F ON P.id = F.person
   ...>   WHERE P.name = 'Bob'
   ...> ) ;
P1.name|P2.name
Al|Bob
Al|Chuck
Al|Frank
Al|Ibrahim
Doug|Bob
Doug|Chuck
Doug|Hamza
Gary|Bob
Gary|Hamza
Gary|Ibrahim
[download]

And so on and so forth, analogously:

sqlite> SELECT P1.name, P2.name
   ...> FROM person P1
   ...> JOIN friend F ON P1.id = F.person
   ...> JOIN person P2 ON F.friend = P2.id
   ...> WHERE P1.id IN (
   ...>   SELECT F.friend
   ...>   FROM person P
   ...>   JOIN friend F ON P.id = F.person
   ...>   WHERE P.id IN (
   ...>     SELECT F.friend
   ...>     FROM person P
   ...>     JOIN friend F ON P.id = F.person
   ...>     WHERE P.name = 'Bob'
   ...>   )
   ...> );
Bob|Al
Bob|Doug
Bob|Gary
Chuck|Al
Chuck|Doug
Chuck|Ed
Chuck|Frank
Frank|Al
Frank|Chuck
Hamza|Doug
Hamza|Gary
Ibrahim|Al
Ibrahim|Gary
[download]

I used SELECT P1.name, P2.name at the top level SELECT for demonstration purposes. In practice you will want SELECT DISTINCT P2.name.

Makeshifts last the longest.