An interpersonal relationship is a relatively long-term association between two or more people. This association may be based on emotions like love and liking, regular business interactions, or some other type of social commitment. Interpersonal relationships take place in a great variety of contexts, such as family, friends, marriage, acquaintances, work, clubs, neighborhoods, and churches. They may be regulated by law, custom, or mutual agreement, and are the basis of social groups and society as a whole. Although humans are fundamentally social creatures, interpersonal relationships are not always healthy. Examples of unhealthy relationships include abusive relationships and codependence. A relationship is normally viewed as a connection between two individuals, such as a romantic or intimate relationship, or a parent-child relationship.

But for us relationships are usually associated with love, liking and family love.
Love:
Interpersonal love refers to love between human beings. It is a more potent sentiment than a simple liking for another. Unrequited love refers to those feelings of love that are not reciprocated. Interpersonal love is most closely associated with interpersonal relationships. Such love might exist between family members, friends, and couples. Throughout history, philosophy and religion have done the most speculation on the phenomenon of love. In the last century, the science of psychology has written a great deal on the subject.
It can be cute like this, but often it's not that easy

and, as we had Valentine's Day lately, something, which is very often told the most romantic song forever:
Friendship
Best friend (or close friend): a person(s) with whom someone shares extremely strong interpersonal ties with as a friend.
Acquaintance: similar to a friend, but sharing of emotional ties isn't present. An example would be a coworker with whom you enjoy eating lunch, but would not look to for emotional support.
Romantic friendship: the very close but non-sexual friendship shared between two friends, often involving physical contact such as hugging, holding hands, and even cuddling.
Soulmate: the name given to someone who is considered the ultimate, true, and eternal half of the other's soul, in which the two are now and forever meant to be together.
Pen pal: a person who shares a "postal" relationship with another and regularly writes via "snail mail". They may or may not have met each other in person and may share either love, friendship, or simply an acquaintance between each other.
Internet friendship: a widely debated and form of friendship or romance which takes place over the Internet.
Comrade: means "ally", "friend", or "colleague" in a military or (usually) left-wing political connotation. This is the feeling of affinity that draws people together in time of war or when people have a mutual enemy or even a common goal. Friendship can be mistaken for comradeship.
This one is quite funny metaphor of friendship.
Family
Interpersonal relationships include kinship and family relations in which people become associated by genetics or consanguinity. These include such roles as father, mother, son, or daughter. Relationships can also be established by marriage, such as husband, wife, father-in-law, mother-in-law, uncle by marriage, or aunt by marriage. They may be formal long-term relationships recognized by law and formalized through public ceremony, such as marriage or civil union. They may also be informal long-term relationships such as loving relationships or romantic relationships with or without living together.

and something more about parent-child relationship:
sources: comics
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