Faith, Eternal Life, Being Born of God, Avoiding Sin - All Linked in 1 John

John the evangelist in his first epistle links being born again to believing (1 John 5:1&4), as one would expect, but also to not committing sin (1 John 3:9 and 5:18), having the seed of God (1 John 3:9), doing righteousness (1 John 2:29), loving one another (1 John 4:7 and 5:1), loving God (1 John 5:1), overcoming the world (1 John 5:4), keeping himself (1 John 5:18), and not being touched by the wicked one (1 John 5:18). 

• 1 John 2:29 If ye know that he is righteous, ye know that every one that doeth righteousness is born of him.
• 1 John 3:9 Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.
• 1 John 4:7 Beloved, let us love one another: for love is of God; and every one that loveth is born of God, and knoweth God.
• 1 John 5:1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
• 1 John 5:4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
• 1 John 5:18 We know that whosoever is born of God sinneth not; but he that is begotten of God keepeth himself, and that wicked one toucheth him not.

Moreover, this is not an isolated theme in John's epistle.  It interconnects with the main theme, which is life through Christ, and our knowledge of having such life, which should give us joy.

• 1 John 1:1-4 That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life; (For the life was manifested, and we have seen it, and bear witness, and shew unto you that eternal life, which was with the Father, and was manifested unto us;) That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ. And these things write we unto you, that your joy may be full.
• ...
• 1 John 5:18-21 We know that whosoever is born of God sinneth not; but he that is begotten of God keepeth himself, and that wicked one toucheth him not. And we know that we are of God, and the whole world lieth in wickedness. And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life. | Little children, keep yourselves from idols. Amen.

This main theme is undeniably about salvation from the punishment due to our sin.  For example, earlier in the conclusion of the epistle, John writes:

1 John 5:13 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God.

Believing on Him is identified as being one of the commandments together with loving one another:

1 John 3:22-23 And whatsoever we ask, we receive of him, because we keep his commandments, and do those things that are pleasing in his sight. And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment.

As can be seen above, in 1 John 5:1 loving God and loving others is a result of being born of God and is thereby linked to believing that Jesus is the Christ.  

Moreover, similarly, being born of God and believing is linked to overcoming the world:

1 John 5:4-5 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith. Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?

I could go on, as the entire book forms an interwoven fabric, but perhaps this suffices to establish.