In both plays Oedipus the King and Antigone what was the importance of kinship?

When faced with injustice, Antigone and Ismene react quite differently - the former aggressively, progressively, and the latter more conservatively. Ismene is not so much afraid of injustice as she is frightened of her own demise - and she cannot bear to incur the wrath of men for fear of being condemned to the same fate as the rest of her family. After watching her father and brothers die, she believes that the best course of action is to lie low and obey. In the case of Ismene, it seems inaction is tied to fear-at least until she willingly offers to die next to Antigone, at which point we realize that she is not so much inactive as she is unsure of her place as a woman. Thus, while Ismene is a figure characterized principally by doubt, Antigone is one who plunges ahead purely on self-belief and her firm convictions about right and wrong. Ultimately, then, because of these fundamental differences in philosophy, they cannot die together, though Ismene wants to. Antigone forbids it - she cannot bear to have her sister tag along when Ismene all along is in the camp of the patriarchs, despite her eleventh-hour shift.