Towards causality graph expansions for local and global causal assessment of flow network models for analytical system resilience explainability

Network models of modern systems such as critical infrastructures, systems of systems, or human cyber-physical systems are key for their modelling, understanding, design, and analysis. Examples include electrical, communication, supply and transport networks, smart homes, or physical access systems. Graph, flow, or engineering-physical models allow by now to assess the influence of disruptions of single or more elements at different system levels to an increasing level of accuracy, transiency, and real time. Also, a plethora of metrics are available to assess system overall risk, e.g., system loss or resilience metrics. The present approach employs the concept of causal graphs and their quantification to reveal levels of dependencies of nodes, which can be extended to cover also edges. This is first conducted at the level of two nodes starting with direct causal dependency chains of first order, and then proposed to be extended to causal elementary models for three elements: chain, fork, and immorality. To assess to which degree two arbitrary nodes of the network are linked by a causal chain of first order, for simplicity a linear dependency model between the nodes is assumed, and its parameters are determined assessing the effect of critical possible risk and resilience weighted disruptions. In this way for each causal elementary graph its relevancy for the overall causal network can be ranked. If this is available for all causal building blocks a procedure can be given how to construct the overall causal graph bottom up avoiding cyclic and undirected structures. The proposed approach is described stepwise as well as equations are given for up to causal chains. The scaling of the approach is assessed. Best local causal models as well an overall causal model can be constructed. For an example the causal graph is constructed and discussed using first order causal chains.