In this thesis we apply graphical statistics models for analyzing causality relations among various international stock markets. We present Graphical models in terms of conditional independence in probability spaces, as opposed to conditional orthogonality of Hilbert spaces, which is the usual presentation of this theory in the literature. We introduce the concept of causality graph with weights to assess for the different degrees of causality relations among markets, i.e., causes coming far from the past are distinguish from causes from the most immediate past. We programmed the construction of causality graphs in R, and apply this methodology to a small sample of 3 major stock markets indices S \& P 500, Nikkei 225 and FTSE 100 to trace the spillover of volatility between them. We repeat this experiment with 11 major stock indices representing industrialized as well as emerging markets all over the world. . The general topic of research is Graphical models for Time Series Analysis and the specific focus will be on Causality Graphs and Financial time series applications. On top of this graph framework we will impose some combinatorics of graphs. Among possible applications: volatility spill over; worldwide causality relations among stock markets