## 3 Materials and Methods
### Granularity of Agents
A Watts-Strogatz small-world network (WSN) stands between regular lattice networks [80] and ER random graphs [81]. A WSN not only shows a small average path length (L), but also a high clustering coefficient (CC). In the analysis of social networks, Average path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes., and clustering coefficient (CC) refers to the extent to which one's friends are also friends [79]. In network science, clustering can be both local and global. The local clustering coefficient of a node is used to measure how connected its neighbors are. It is represented as the number of links between the node's neighbors divided by the total number of possible links between its neighbors. The global clustering coefficient is used to measure how many nodes tend to cluster together in the entire network. It is defined according to the types of triplets in the network. A triplet is composed of a central node and two of its neighbors. If its neighbors are connected as well, it is a triangle (a closed triplet). If its neighbors are not connected, it is called an open triplet. The global clustering coefficient is the number of triangles in a network divided by the total number of triplets (both open and closed). The L value of a WSN grows proportionally to the logarithm of the number of nodes N in the network [67], and the CC value of a WSN tends to \(\frac{3}{4}\) in case of large N [82].The degree distribution of a small-world network obeys the familiar Poisson distribution, and the shape of the Poisson distribution falls off exponentially [67]. While other types of networks, such as regular lattice, Erdos-Renyi (ER) random graph model, and the Watts-Strogatz (WSN) model do not show power laws, approximately a number of real-world networks fall into the class of scale-free networks, meaning that they possess power-law degree distributions. In comparison with small-world networks, this power-law distribution falls off more gradually than an exponential one, allowing for a few nodes of the very high degree to exist (i.e., hubs). Because these power-laws are independent of any characteristic scale, such a network with a power-law degree distribution is called a scale-free network. In terms of average path length, a scale-free network resembles to a small-world one, but is a lower clustering coefficient [80]. The Barabasi-Albert model, known as preferential attachment network, is one of several suggested models that create scale-free networks. This model integrates two important general concepts of: Growth and preferential attachment, which widely exist in real networks. Growth signifies that the number of nodes in the network intend to increase over time. Preferential attachment means that the more links a node have, the more likely it is to get newer links. Higher-degree nodes have a higher ability to get links added to the network [66]. In this paper, both of these network structures have been separately used to simulate the social environment where adopters interact and a technology is diffused.