It is undoubtedly that everything in this world are related and nothing independently exists. Entities interact together to form groups, resulting in many complex networks. Examples involve functional regulation models of proteins in biology, communities of people within social network. Since complex networks are ubiquitous in daily life, network learning had been gaining momentum in a variety of discipline like computer science, economics and biology. This call for new technique in exploring the structure as well as the interactions of network since it provides insight in understanding how the network works and deepening our knowledge of the subject in hand. For example, uncovering proteins modules helps us understand what causes lead to certain disease and how protein co-regulate each others. Therefore, my dissertation takes on problems in computational biology and social network: cancer informatics and cascade model-ling. In cancer informatics, identifying specific genes that cause cancer (driver genes) is crucial in cancer research. The more drivers identified, the more options to treat the cancer with a drug to act on that gene. However, identifying driver gene is not easy. Cancer cells are undergoing rapid mutation and are compromised in regards to the body's normally DNA repair mechanisms. I employed Markov chain, Bayesian network and graphical model to identify cancer drivers. I utilize heterogeneous sources of information to discover cancer drivers and unlocking the mechanism behind cancer. Above all, I encode various pieces of biological information to form a multi-graph and trigger various Markov chains in it and rank the genes in the aftermath. We also leverage probabilistic mixed graphical model to learn the complex and uncertain relationships among various bio-medical data. On the other hand, diffusion of information over the network had drawn up great interest in research community. For example, epidemiologists observe that a person becomes ill but they can neither determine who infected the patient nor the infection rate of each individual. Therefore, it is critical to decipher the mechanism underlying the process since it validates efforts for preventing from virus infections. We come up with a new modeling to model cascade data in three different scenarios.