Each divine person is God, whole and entire. Since all of the Father is given to the Son, the Son is God whole and entire just as the Father is God whole and entire. So too with the Spirit. Jesus is God, the Father is God and the Holy Spirit is God. The Catechism explains it this way:
“The Trinity is One. We do not confess three Gods, but one God in three persons, the "consubstantial Trinity". The divine persons do not share the one divinity among themselves but each of them is God whole and entire” (CCC 253)
Their giving is their unity. The more we share of ourselves the deeper our friendships are, the greater the unity among our friends. The Trinity is the fullness of love since each person shares all that they are with each other. Therefore the Trinity is perfect love and perfect friendship. In God this is total, infinite and perfect, therefore God is a perfect unity and all is not just shared, but each person is God.
There are other words which can be used to expressed the unity of God, which are substance, essence, nature and being. These words are interchangeable when it comes to the Trinity. Each word is used in its own context. The Catechism states, "The Church uses the term "substance" (rendered also at times by "essence" or "nature") to designate the divine being in its unity” (CCC 252).
“The Trinity is One. We do not confess three Gods, but one God in three persons, the "consubstantial Trinity". The divine persons do not share the one divinity among themselves but each of them is God whole and entire” (CCC 253) This is the ultimate friendship. Better friends share more of themselves with each other. Each divine person shares all of themselves with each other divine person and so the Trinity is one God. There are various words we can use to designate God's unity, "The Church uses the term "substance" (rendered also at times by "essence" or "nature") to designate the divine being in its unity” (CCC 252).