## The Vation Ventures Glossary

# Directly-Follows Graph: Definition, Explanation, and Use Cases

The concept of a Directly-Follows Graph is a fundamental building block in the field of Process Mining. This term refers to a specific type of graph that is used to represent and analyze the sequential relationships between activities in a process. The Directly-Follows Graph is a crucial tool in the arsenal of process miners, enabling them to visualize and understand the flow of activities in a process, identify bottlenecks and inefficiencies, and derive insights for process improvement.

Understanding the Directly-Follows Graph requires a basic familiarity with the principles of Process Mining, a discipline that leverages event log data to model, analyze, and optimize business processes. The Directly-Follows Graph is one of the many techniques used in Process Mining to represent and analyze process data. This article will delve into the intricacies of the Directly-Follows Graph, providing a comprehensive understanding of its definition, explanation, and use cases.

## Definition of Directly-Follows Graph

A Directly-Follows Graph, in the context of Process Mining, is a directed graph that represents the sequence of activities in a process. Each node in the graph represents an activity, and each directed edge represents the sequence in which activities occur. If there is a directed edge from activity A to activity B, it means that activity A directly follows activity B in the process.

The Directly-Follows Graph is constructed based on an event log, which is a record of the sequence of activities in a process. The event log provides the raw data needed to build the Directly-Follows Graph. Each entry in the event log corresponds to an activity in the process, and the order of entries in the log determines the directed edges in the graph.

### Components of a Directly-Follows Graph

The Directly-Follows Graph consists of two main components: nodes and edges. The nodes represent the activities in the process. Each node is labeled with the name of the activity it represents. The edges represent the sequence of activities. Each edge is directed from one node to another, indicating that the activity represented by the first node directly follows the activity represented by the second node in the process.

The edges in a Directly-Follows Graph can also be weighted to represent the frequency of the sequence. The weight of an edge is determined by the number of times the sequence of activities represented by the edge occurs in the event log. This provides additional information about the frequency and regularity of the sequence, which can be useful in analyzing the process.

### Representation of a Directly-Follows Graph

A Directly-Follows Graph can be represented visually as a diagram, or textually as a matrix. The visual representation is more intuitive and easier to understand, but the textual representation can be more precise and detailed. The choice of representation depends on the complexity of the process and the needs of the analysis.

In a visual representation, the nodes are depicted as circles or squares, and the edges are depicted as arrows. The direction of the arrow indicates the sequence of activities. In a textual representation, the nodes are listed in a matrix, and the edges are represented by numbers in the matrix. The number in the cell at the intersection of row A and column B indicates the number of times activity A directly follows activity B in the process.

## Explanation of Directly-Follows Graph

The Directly-Follows Graph provides a visual representation of the sequence of activities in a process. It shows how activities are interconnected, and how the process flows from one activity to another. This makes it a powerful tool for understanding and analyzing the process.

However, the Directly-Follows Graph is more than just a visual representation. It also provides a mathematical model of the process, which can be used for quantitative analysis. The nodes and edges in the graph can be analyzed using graph theory, a branch of mathematics that studies the properties of graphs. This allows for a deeper understanding of the process, beyond what can be seen in the visual representation.

### Understanding the Sequence of Activities

The main purpose of the Directly-Follows Graph is to represent the sequence of activities in a process. The graph shows which activities directly follow each other, and in what order. This provides a clear and concise overview of the process flow.

By analyzing the sequence of activities, one can identify patterns and trends in the process. For example, if a certain sequence of activities occurs frequently, it may indicate a common workflow or routine. On the other hand, if a certain sequence rarely occurs, it may indicate an exception or anomaly in the process.

### Identifying Bottlenecks and Inefficiencies

Another important use of the Directly-Follows Graph is to identify bottlenecks and inefficiencies in the process. A bottleneck is a point in the process where the flow of activities slows down or stops, causing delays and inefficiencies. In the Directly-Follows Graph, a bottleneck can be identified as a node with a high incoming degree but a low outgoing degree.

By identifying bottlenecks, one can take steps to improve the process. For example, if a certain activity is causing a bottleneck, one could try to streamline that activity, or find a way to bypass it. Similarly, if a certain sequence of activities is inefficient, one could try to rearrange the sequence, or replace some activities with more efficient ones.

## Use Cases of Directly-Follows Graph

The Directly-Follows Graph is a versatile tool that can be used in a variety of contexts and applications. Its main use is in Process Mining, where it is used to model and analyze business processes. However, it can also be used in other fields, such as computer science, operations research, and network analysis.

In Process Mining, the Directly-Follows Graph is used to visualize and analyze the sequence of activities in a process. It can be used to identify patterns and trends, detect anomalies and outliers, and derive insights for process improvement. It can also be used to compare different processes, or different versions of the same process, to identify differences and similarities.

### Process Discovery

One of the main use cases of the Directly-Follows Graph is in process discovery, which is the task of discovering the underlying process model from event log data. The Directly-Follows Graph provides a visual representation of the process, which can help in understanding the process and deriving the process model.

In process discovery, the Directly-Follows Graph is often used as a starting point. The graph is constructed based on the event log, and then refined and adjusted based on additional information and constraints. The final process model is a refined version of the Directly-Follows Graph, which accurately represents the process and satisfies all constraints.

### Conformance Checking

Another use case of the Directly-Follows Graph is in conformance checking, which is the task of checking whether the actual execution of a process conforms to the prescribed process model. The Directly-Follows Graph represents the actual execution of the process, and can be compared with the process model to check for conformance.

In conformance checking, the Directly-Follows Graph is compared with the process model to identify deviations and discrepancies. If the graph matches the model, it means that the process is conforming to the model. If there are deviations, it means that the process is not conforming to the model, and further investigation is needed to identify the causes of the deviations.

### Performance Analysis

The Directly-Follows Graph can also be used for performance analysis, which is the task of analyzing the performance of a process in terms of efficiency, effectiveness, and quality. The graph provides a visual representation of the process flow, which can be used to identify bottlenecks and inefficiencies, and derive insights for process improvement.

In performance analysis, the Directly-Follows Graph is often augmented with additional information, such as timestamps and resources, to provide a more detailed view of the process. The graph can be analyzed using various performance indicators, such as cycle time, throughput, and utilization, to assess the performance of the process.