# Optimization of Clustering in Wireless Sensor Networks: Techniques and Protocols
## 4 The Fundamentals of Clustering
### Clustering Characteristics  
Some attributes of clustering methods rely on the internal cluster structure to categorize different clustering protocols. Figure 3 shows a set of these attributes and can be applied in various WSN clustering protocols. Some of each attribute's definitions and uses in every clustering technique are summarized.  
* Inter-cluster head connectivity: Reflects the ability of SNs or CHs to establish communication with the BS. The clustering scheme must provide intermediate routing routes to the BS if the CH cannot establish long-distance communication;
* Cluster count: Refers to the number of clusters developed in each round; the higher the number of CHs, the smaller the cluster distribution size and the better the energy conservation. CH selection in some clustering methods is pre-assigned, meaning that the CHs can be randomly selected, resulting in different numbers of clusters;
* Cluster size: The optimum path length between the individual nodes and distance from the CH in a cluster. The smaller the cluster size, the better the energy usage, as the transmission distance and CH load are effectively reduced. The cluster size is fixed in some clustering methods, especially when clusters are fixed throughout their service life, but some clustering methods have a variable size for each cluster;
* Cluster density: Refers to the number of ordinary nodes in a cluster; reduction in energy usage by the CHs in dense clusters is a tedious task. Hence, most clustering methods rely on fixed clustering and opt for sparse cluster density (cluster density is variable for dynamic clustering methods);
* Message count: Refers to the required number of message transmissions for CH selection. The higher the message count, the more energy usage required for the CH selection procedure. Most non-probabilistic algorithms require message transmission for CH selection;
* Stability: Clustering schemes are adaptive if the members of a cluster are not fixed; otherwise, they are considered fixed because the cluster count cannot be varied during the process of CH selection. Fixing the cluster count improves the stability of an SN;  
Figure 3: Clustering characteristics in WSNs.  
Clustered WSNs can be categorized into homogeneous and heterogeneous classes based on the type and function of the SNs in the network [33]. In the homogeneous class, all SNs exhibit similar features, processing, and hardware capabilities. The CH is normally rotated among the component SNs to ensure uniform energy usage within the network. On the other hand, the heterogeneous class contains two or more types of SNs: the first type is those with complex hardware and greater processing capabilities that are mainly used to create some sort of backbone inside the WSN [34], which are designed to serve as the CHs and can act as data collectors and data processing centers, while the second type is the participating sensors developed with lower capabilities, which are used to sense the desired parameters in the field.  
Cluster formation remains the most interesting aspect of studies on clustering protocols; the other issues of concern are those relating to the number of clusters to be formed, the formation of the cluster members, and the size of each cluster. Energy consumption in sensor networks is believed to be dependent on the number of clusters, size of the clusters, and cluster density. Cluster size and cluster density are directly related to the cluster count, because the lower the cluster count, the more energy needed to manage the increased number of cluster members. Dense clusters affect the stability of the sensor network; it is important to increase the cluster count to reduce the cluster size and cluster density. One of the challenges in clustered WSNs is optimizing the cluster density, cluster count, and cluster size to improve the network stability and lifespan.