Because of the international principle of sovereignty, there is no external force requiring extradition from one country to another. In Austria, Brazil, People’s Republic of China, Republic of China, Czech Republic, France, Germany, Japan, Norway, Russia, Switzerland and Syria, you cannot legally be extradited if you are a citizen of that country, since the extradition laws of those countries preclude extraditing citizens.
Whether or not an extradition request will be honored in the remaining cases depends on the laws of that country, especially whether the law allows vs. requires (vs. forbids) extradition. The primary consideration is whether a treaty exists between the sending and receiving countries: see this article
Extradition treaties are in the nature of a contract and by operation
of international law, “[a] state party to an extradition treaty is
obligated to comply with the request of another state party to that
treaty to arrest and deliver a person duly shown to be sought by that
state (a) for trial on a charge of having committed a crime covered by
the treaty within the jurisdiction of the requesting state, or (b) for
punishment after conviction of such a crime and flight from that
state, provided that none of the grounds for refusal to extradite set
forth in [the treaty] is applicable.
18 USC 3181 mandated that you may not be extradited from the US unless the receiving country has an extradition treaty with the US. In a limited set of contexts (crimes of violence against US nationals committed by persons who are not US citizens, nationals or LPRs), in lieu of a treaty and "in the exercise of comity", a person might also be extradited. This section then says when extradition may be considered, and at what point in the proceeding, the extradition shall be performed. The law of extradition in Norway is different (much more complex rules). Apart from the prohibition of extraditing Norwegian nationals (Norsk statsborger), there is a requirement that the crime be punishable in Norway by more than a year in prison; there is a prohibition against extraditing if there is a "conflict with basic humanitarian considerations, especially because of their age, health or other personal circumstances" (current law, art. 7)... and so on. Bolivia, on the other hand, allows extradition of its own nationals to the US, pursuant to their treaty with the US, for a specific list of crimes:
murder; voluntary manslaughter; kidnaping; aggravated assault; rape;
sexual offenses involving children; armed robbery; offenses related to
the illicit traffic in controlled substances; serious offenses related
to terrorism; serious offenses related to organized criminal activity;
fraud against the government or involving multiple victims;
counterfeiting of currency; offenses related to the traffic in
historical or archeological items; offenses punishable in both States
by deprivation of liberty for a maximum period of at least ten years
In principle, any nation could in their extradition treaty exclude extradition of certain dual nationals, if they had a political motivation to do so.