Suppose two people $A$ and $B$ belong to a connected component of the graph. Let the path connecting them be $A-v_1-v_2-\ldots-v_n-B$. We will prove by induction that after each of $v_1,v_2,\ldots,v_n$ arranges a party, $A$ and $B$ will know each other. For $n=1$, the statement obviously holds. Suppose it is true for smaller $n$. Let $v_i$ be the last person arranging the party. Since each of $v_1,v_2,\ldots,v_{i-1}$ and $v_{i+1},v_{i+2},\ldots,v_n$ has arranged a party, by the induction hypothesis, $v_i$ knows $A$ and $B$. Therefore $A$ and $B$ are introduced in $v_i$'s party. After each person has arranged at least one party, if two people do not know each other, then they must belong two different components of the graph. Hence they will never be introduced in any party.