# A Survey on Cyber Risk Management for the Internet of Things
## 4 Cyber Risk Assessment for IoT Survey Results
### IoT Cyber Risk Calculation
#### 4.2.1 Use of Graph Modelling  
Within cyber risk management, graph modelling represents how an attacker can infiltrate a network using graphical models to show the potential attack paths that could be used, using such concepts as nodes, edges, and dependencies. It is very common to model data flow and interaction within networks to better understand the areas with high risk, and how a risk could propagate to other nodes. As an example, [PERSON] et al. [62; 63] formulate IoT network topologies using network mapping to form a connected graph to show the relationships between nodes. Not only this, but the authors also use plotted comparative graphs to show risk exposure scores to different attacks [63]. Bayesian networks are acyclic graph models that are probabilistic, depending on random variables and dependency. Due to IoT data not always been completely known, Bayesian networks can be used to infer the posterior probability distribution of unobserved variables, given evidence, or observed values for other variables in the network [44]. [PERSON] et al. [44] use Bayesian networks to visualise smart city states and connections of the nodes and estimate probabilities that may not be known. To account for changes over time, dynamic Bayesian networks can be used as a temporal extension to better model probabilities, which can help in providing updated estimates for IoT systems. In connection, [PERSON] et al. [71] propose a generic IoT risk assessment model using a weighted acyclic graph upon modelling information flow within an IoT network. The weighting system signifies priority paths and high impact, accounting for the increased risk in more vulnerable parts of an IoT network. The links between nodes reflect the dependency of one node or another depending on link direction, with nodes also being able to control other links. To demonstrate attack scenarios, an attack vector is formed which consists of aggregated likelihood and cumulative business impact at an IoT node. Figure 5: A visual breakdown of the number of papers per IoT risk? concept. For example, of the 39 collected papers, 12 of them fit into our survey’s use of graph modelling category. This allows the risk of a directly attacked node/edge to be computed using the aggregated risk of a node due to other nodes of differing dependency. A flow network is a directed graph where a flow starts from a source node and reaches a sink node with no dispersion. [PERSON] et al. [45] use these graphs to solve the question of how much IoT risk an organisation can mitigate. The risk value of each IoT asset can be used to find the total maximum flow, given the degree of risk mitigation for a mechanism. In contrast, [PERSON] et al. [55] use oriented graphs (directed graphs with no symmetric pair of directed edges) with arc identification representing compromised IoT nodes alongside the possibility of exploiting the vulnerability of the node. The criticality of compromise is computed for each node with the sum of criticality values to reflect the total risk. [PERSON] et al. [59] propose an IoT algorithm that can model and visualise the dynamic changes that occur in a smart home network topology. The algorithm also includes a study of the propagation of infection using attack graphs. A smart home network topology is simulated, generating a vector for a risk input parameter, which is followed by the IoT node and edge generation. The algorithm then visualises a smart home network topology with the given IoT risk metrics while considering malfunctioning or intermittent availability out of a user's control. To find IoT risk, the algorithm uses a conditional probability function which determines the state of risk, describing these states as vulnerable, infected, quarantined, healthy and intermittent. [PERSON] and [PERSON] [53] propose an IoT graphical model that captures multi-stage and multi-host IoT attacks through the linking of vulnerabilities found within networks, using graph modelling to uncover vulnerability patterns.