How do each of the four forms of suicide relate to specific levels of social integration and social regulation?
Emile Durkheim came up with a theory of suicide in which it comes in four basic types.
1. Egoistic suicide, the most common, occurs when people become so socially isolated that they are unable to function. Durkheim claimed that this was because the individual was highly selfish, but there's little evidence that depressed people are actually particularly selfish---they are just particularly isolated. They lack systems of social support to cope with the stresses of life, and may also be genetically predisposed to be more sensitive to those stresses.
2. Altruistic suicide, which Durkheim described as the opposite---people who in a sense becomes too socially integrated. A better way of putting it might be that they become too tribal; they deeply connect their sense of identity with a particular narrow in-group and ignore or even hate those in the out-groups. This is the source of suicide bombing---a terrorist cell is a very close-knit social tribe and hates the out-group that is the target of the terrorism.
3. Anomic suicide, which comes from a sudden disruption in one's life; usually it is a negative disruption (unemployment, a death in the family), but positive disruptions can have a similar effect (winning the lottery). Durkheim characterized this as a loss of regulation; the social rules under which the person lived no longer apply, and they are unable to adapt to the shift.
4. Fatalistic suicide, which comes from what Durkheim characterized as social over-regulation---what we might more conventionally call oppression. This kind of suicide occurs when people are so controlled by outside forces that they feel they have lost all autonomy in their lives, and they give up and decide they'd rather die than go on being controlled like a puppet.
Durkheim's taxonomy of suicide is useful, but it is hampered by his insistence that it is only these two factors---either too little or too much social integration, either too little or too much social regulation. There are good reasons to think that a balanced level of integration and regulation are beneficial for a variety of reasons; but Durkheim's theory would seem to predict a whole lot of suicides that don't happen---people who are oppressed often don't kill themselves, not everyone who is lonely or even depressed becomes suicidal, many people undergo positive and negative disruptions in their lives but survive or even thrive, and many tight-knit social groups are harmless and nonviolent. It reminds me of the joke about the macroeconomist who successfully predicted nine of the last five recessions.
Durkheim has no good explanation for why suicide is as rare as it is; for that we need more information---personality differences, more detailed social structure information, and even things as simple as the level of access to firearms.