Square Complexity Metrics for Business Process Models

Overview

This page describes a set of square complexity metrics, proposed in paper "Square Complexity Metrics for Business Process Models".
The authors porpose a simple yet practical square metrics for describing complexity of a BP model based on the Durfee and Perfect square concept. These metrics are easy to interpret and provide some basic information about the structural complexity of the model.
In addition, a set of basic metrics (for example count of different BPMN elements) were implemented, which can be used as basis for more complex metrics.

Implemented metrics

All of the implemented metrics are available in package bpmn_diagram_metrics. The following list provides short description of each metric and the corresponding Python method:

• Total Number of Start Events metric (method TNSE_metric) - evaluates a total number of start events in the BPMN model.
• Total Number of Intermediate Events metric (method TNIE_metric) - evaluates a total number of intermediate events in the BPMN model.
• Total Number of End Events metric (method TNEE_metric) - evaluates a total number of end events in the BPMN model.
• Total Number of Events metric (method TNE_metric) - evaluates a total number of end events in the BPMN model.
• Number of Activities metric (method NOA_metric) - evaluates a total number of activities in the BPMN model.
• Number of Activities and Control flow elements metric - evaluates a total number of activities and control flow elements in the BPMN model.
• Number of Activities, Joins and Splits metric (method NOAJS_metric) - evaluates a total number of activities, joins and splits in the BPMN model.
• Number Of Nodes metric (method NumberOfNodes_metric) - evaluates a total number of nodes in the BPMN model.
• Gateway Heterogenity metric (method GatewayHeterogenity_metric) - evaluates the value of the Gateway Heterogenity metric (number of different types of gateways used in a model).
• Coefficient of Network Complexity metric (method CoefficientOfNetworkComplexity_metric) - evaluates the value of the Coefficient of Network Complexity metric (ratio of the total number of arcs in a process model to its total number of nodes).
• Average Gateway Degree metric (method AverageGatewayDegree_metric) - evaluates the value of the Average Gateway Degree metric (average of the number of both incoming and outgoing arcs of the gateway nodes in the process model).
• Durfee Square metric (method DurfeeSquare_metric) - evaluates the value of the Durfee Square metric. Durfee Square equals d if there are d types of elements which occur at least d times in the model each, and the other types of elements occur no more than d times each.
• Perfect Square metric (method PerfectSquare_metric) - evaluates the value of the Perfect Square metric. Given a set of element types ranked in decreasing order of the number of their instances, the PSM is the (unique) largest number such that the top p types occur (together) at least p2 times.