Andersen never married and never had any children. He was, however, closely entwined with many families, friends, and children that filled his life with love. He expressed romantic interest in many people during his life, a few can be seen on the "Loves" page, but there exists more than just romantic love.
Eros- sexual passion and lust, leaning more towards physical love rather than romantic. Eros is also the name of the Greek god of love and is characterized as a positive and life-giving force but can also lead to obsessive love. It can also be broadened to include a philosophical yearning for the knowledge of the beautiful, good, and true.
Philia- affectionate love between equals, often referring to friendship or brotherly love (like Philadelphia, the city of brotherly love). Traditionally interpreted as a more virtuous type of love that is separated from a love that includes sexual attraction that is built on honesty and understanding.
Agape- an unconditional, selfless love that refers to familial love, such as the love between child, parents, spouse, or community. Also can refer to a form of Christian love, referencing Jesus or God’s love towards his creation.
Ludus- playful love indicated my playful behavior and budding feelings. Think of “puppy love” at the start of a new relationship or crush.
Storge- unconditional love, often for a family member, a non-romantic form of love.
Philautia- deep self-love, can mean having self-esteem, caring for yourself, seeing yourself as valuable, and practicing self-awareness.
Pragma- compassionate, long-term love that exists in a longer-term or committed relationship. Eros can become pragma given time and commitment to a healthy relationship.
As with any historical figure, it is impossible to say where Andersen would fall in today's understanding of love. For one thing, he lived during the Romantic era, where men and women were kept separate outside of specific social occasions. During this time, there was an ideal of a "sensitive friendship" where two men or women grew in a special friendship intended to help them both mature and grow. Letters within this pair were expected to be numerous and contain intimate thoughts and wishes. These friendships were a type of emotional training for marriage as it formed a close partnership between two people. Andersen strove to cultivate this kind of friendship with many people, most of all with Edvard Collin. In his later years, Andersen tried to cultivate a sort of platonic-Socratic relationship with younger men where he gained companionship and new friends, and the younger men, such as Harald Scharff and Edvard's son Jonas, gained mentorship.
In the end, Andersen experienced familial love, platonic love, and romantic love with men and women, yet none of these relationships were really fulfilled. After Andersen left for Copenhagen, he rarely exchanged letters with his mother and was abroad when she died in 1833 in a poor house. He maintained many friendships through floods of letters, yet he had just as many enemies and critics, including some friends-turned-enemies like Charles Dickens. As for romantic love, most of the people he pursued were already unreachable because of their different social statuses, their gender, and the fact that a handful were already engaged when he began to court them. However, Andersen died surrounded and cared for by friends with several godchildren that all adored him and a legacy of writing that would touch generations to come.