For each clique $$\mathcal{C}$$ in an undirected graph, a factor $$\phi(\mathcal{C})$$ called the **Clique Potential** measures the affinity of the variables in that clique. A clique is a subset of nodes in the graph where every two distinct nodes are directly connected by an edge. Together, these factors form the **unnormalized probability distribution**: $$\tilde{p}(\mathbf{x}) = \prod_{\mathcal{C}\in \mathcal{G}}\phi(\mathcal{C})$$

University of Connecticut

Google

Undirected Models (AKA Markov Random Fields/MRF/Markov Networks) have typical graph structure but the vertices are undirected.

Undirected Models

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

While a directed graph structure is suitable for a set of random variables where there is clear causality, an undirected graph structure is better fit for a situation where dependence upon random variables flows in multiple directions.

For example, a model showing the health status (probability of having a cold) of you, your roommate, and a coworker could be represented with an undirected graph. Your health status would be a node with undirected vertices connected to your coworker's and roommate's health status respectively, as you can get either of them sick, either one of them could get you sick, but they cannot *directly get each other* sick.

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