In 2015

the United Nations launched the 17 Sustainable Development Goals (SDGs) as an integrated approach to tackle global challenges

aiming for a better and more sustainable future for the planet. Despite their comprehensive framework

the SDGs' implementation has encountered difficulties due to their intricate interdependencies and complex interactions. This paper introduces a versatile and innovative framework to examine the SDGs' interconnected nature

utilizing three mathematical models: the SDG Interaction Network Model

the SDG Prioritization Model

and the Markov-based Link Prediction Model. These models explore the dynamics between the SDGs

revealing how achieving one goal can either support (through synergistic relationships) or hinder (via trade-offs) the progress of others. By prioritizing different goals

we observe fluctuations in the network's structure and the individual goals' scores

interpreted as shifts in priority and network link adjustments. This analysis sheds light on the evolving network of SDGs

offering valuable insights into goal relationships and suggesting strategic priorities to enhance the effectiveness of the UN's agenda.