In this paper, we propose a new comprehensive realistic cyber security dataset of IoT and IIoT applications, called Edge-IIoTset, which can be used by machine learning-based intrusion detection systems in two different modes, namely, centralized and federated learning. Specifically, the proposed testbed is organized into seven layers, including, Cloud Computing Layer, Network Functions Virtualization Layer, Blockchain Network Layer, Fog Computing Layer, Software-Defined Networking Layer, Edge Computing Layer, and IoT and IIoT Perception Layer. In each layer, we use new emerging technologies that satisfy the key requirements of IoT and IIoT applications, such as, ThingsBoard IoT platform, OPNFV platform, Hyperledger Sawtooth, Digital twin, ONOS SDN controller, Mosquitto MQTT brokers, Modbus TCP/IP, …etc. The IoT data are generated from various IoT devices (more than 10 types) such as Low-cost digital sensors for sensing temperature and humidity, Ultrasonic sensor, Water level detection sensor, pH Sensor Meter, Soil Moisture sensor, Heart Rate Sensor, Flame Sensor, …etc.). Furthermore, we identify and analyze fourteen attacks related to IoT and IIoT connectivity protocols, which are categorized into five threats, including, DoS/DDoS attacks, Information gathering, Man in the middle attacks, Injection attacks, and Malware attacks. In addition, we extract features obtained from different sources, including alerts, system resources, logs, network traffic, and propose new 61 features with high correlations from 1176 found features. After processing and analyzing the proposed realistic cyber security dataset, we provide a primary exploratory data analysis and evaluate the performance of machine learning approaches (i.e., traditional machine learning as well as deep learning) in both centralized and federated learning modes.