To address the limitations of carbon emission flow modeling in the safety analysis of integrated electricity-gas system (IEGS) and explore system security monitoring theories and methods centered on a carbon flow perspective. This paper proposes the concept

model

and computational analysis of the carbon emission security region (CESR) for IEGS. First

the CESR model for IEGS under N-0 security constraints is established. Subsequently

the mathematical coupling mechanism between CESR and the energy flow security region (EFSR) is investigated

with geometric correlations in high-dimensional space analyzed. Next

a quantitative model for system total carbon emission capacity limits is developed. Furthermore

the concept of CESR security boundaries and a visual dimensionality- reduction observation method are proposed. Furthermore

the mathematical relationship between the carbon emission capacity and the total supply capability is explored

revealing that it is not a simple proportional linear relationship and must be analyzed specifically for the topology and operational conditions of the individual IEGS. Finally

case studies validate the effectiveness of the proposed model

the concepts and computational frameworks of the maximum carbon-constant total supply capability (MAX_CTSC) and minimum supply- constant total carbon emission capacity (MIN_STCE) are established based on these studies. This work ultimately provides theoretical foundations and decision-making tools for achieving security-low carbon-high supply synergy of IEGS under the "dual carbon" goals.