The Internet of Things (IoT) has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses. Social network analysis (SNA) is a good example that has recently gained a lot of scientific attention. It has its roots in social and economic research, as well as the evaluation of network science, such as graph theory. Scientists in this area have subverted predefined theories, offering revolutionary ones regarding interconnected networks, and they have highlighted the mystery of six degrees of separation with confirmation of the small-world phenomenon. The motivation of this study is to understand and capture the clustering properties of large networks and social networks. We present a network growth model in this paper and build a scale-free artificial social network with controllable clustering coefficients. The random walk technique is paired with a triangle generating scheme in our proposed model. As a result, the clustering control mechanism and preferential attachment (PA) have been realized. This research builds on the present random walk model. We took numerous measurements for validation, including degree behavior and the measure of clustering decay in terms of node degree, among other things. Finally, we conclude that our suggested random walk model is more efficient and accurate than previous state-of-the-art methods, and hence it could be a viable alternative for societal evolution.

In recent years, social networks have gained popularity and the attention of researchers working in different fields of science [

The motivation of our study is to capture the basic network properties of large-scale social networks [

The main contributions of this study are given below.

We propose a scale-free, artificial social network generation model that is purely local, requiring no global selection of nodes, or any initial network.

The random walk model is used to generate artificial networks that incorporate the properties of small-world and scale-free networks, with the additional advantage of having an adjustable clustering coefficient.

Using a visual analytics method introduced earlier [

The benefits of this study are given below.

It will be helpful to researchers who wish to learn the methods of generating artificial networks.

The researchers who want to understand the structural properties of a network.

This research is also beneficial for several network mining problems including extrapolation, sampling, model testing, etc.

In Section 2, we discussed standard network measures. Subsequently, we present prior studies on scale-free and small-world networks. we discussed classic random walk models (along with their limitations) and also the problem statement. We discussed our proposed model in Section 3. Section 4 offers detailed experimental results and a discussion related to this study. The conclusion and future work from this study are presented in Section 5.

This section is divided into three subsections. In Section 2.1, we discuss classic standard measures in networks. In Section 2.2, we discuss the scale-free and small-world concepts along with their limitations. In Section 2.3, we discuss a few studies related to the classic random walk.

In this section, we first discuss the standard network measures, and then, we discuss the relationships between these network measures.

Perhaps the most important property of a node in a network is its degree. Node degree illustrates the number of nodes that are directly connected. Generally, nodes may have any whole-numbered degree (including zero, for an isolated node that is not connected to any other). In a network, the degree will be twice the number of edges. In most networks, every edge is usually incident to two different nodes.

The degree distribution is how the degrees of the nodes arise across the network, i.e., the number of nodes in a network with degree 1, degree 2, and so forth. In short, any network will have the largest (maximal) and the smallest (minimal) degree.

The clustering coefficient is used to measure the grouping, or the triadic closure, in a graph. It is a calculation of the number of triangles in the network. More simply, it is a measure of the extent to which one’s friends are also friends of each other:

The path length (geodesic) is the average distance between two nodes chosen at random. The path length lies in the range between

We divided this section into three distinct subsections. In Section 2.2.1, we discuss a few studies related to the small-world network. In Section 2.2.2, we discuss two basic concepts: scale-free and PA. In Section 2.2.3, we performed a survey and compare various studies in tabular form.

The patterns in several networks, such as the social network [

Saramäki et al. [

In the growth phase, at each timestamp, a new node is added with

During PA, the attachment preference for a node is only assigned to high-degree nodes.

According to the power law, when a new node is about to join a network, it is preferably linked to the current nodes that constitute a large part of the links in the network. The computed probability,

BA model provides the key information for scale-free networks, and the WS model has small-world properties [

Model | Year | Diameter | Adjustable clustering | Scale-free | Local info |
---|---|---|---|---|---|

Erdos | 1960 | ||||

Watts-Strogatz | 1998 | ||||

Barabasi & Albert | 1999 | ||||

Newman | 2001 | ||||

Holme et al. [ |
2002 | ||||

Vazquez | 2003 | ||||

Newman | 2011 | ||||

Amorim et al. [ |
2016 | ||||

H. Shah et al. [ |
2017 | ||||

Matsumura et al. [ |
2018 |

In this section, we first discuss a few classic random walk processes, and then, we discuss the problem statement.

Generally, in real networks, adding a new node would not require global information about the network. Several studies have been conducted in which local network information is used to spawn scale-free networks without using global information [

Katzir et al. [

In our study, we consider the growth and evolution of networks as a fundamental problem in network science, especially because networks constantly change over time. The random walk process is helpful for the construction and growth of the network. We observed from earlier studies that although triadic closure is helpful for the growth of a network, the incorporation of dynamic triadic closure will produce more powerful and bigger networks. After reviewing several research ideas, our key findings are as follows.

The scale-free concept and the power law, including directing rules, are helpful in the growth and the construction of an artificial network.

An algorithm is efficient if it uses its local information. The connections are also important in a local network. The introduction of local immunization strategies is effective for the growth of a network.

In this section, we suggest a random walk model for the growth of a network where the clustering coefficient can be estimated and adjusted dynamically. The proposed model is closely related to the recent studies related to growing networks through random walk models by Amorim et al. [

We denote as

There are three basic steps involved in this model.

Hence, in our proposed algorithm we have used the following design parameters:

In this section, we present our experimental results in detail. We have divided this section into two subsections. At first, we have discussed the preliminaries of the power law, and then we have discussed the achieved experimental results.

First, we need to define the initial seed and

Hence, to address this issue, we have designed a ring lattice with

In this section, we have discussed experimental results in terms of degree distribution and triadic closure. We performed a series of experiments using Network X [

The emergence of a scale-free structure during the growing process is discussed in this section.

Parameters | No Restrat Random Walk (NRRW) model [ |
RW model [ |
Our model |
---|---|---|---|

Nodes | 7640 | 7413 | 7640 |

Edges | 274865 | 2244905 | 2777029 |

Average degree | 2303 | 352 | 1271 |

Clustering coefficient | 0.09 | 0.61 | 0.87 |

Average path length | * | * | * |

Parameters | Nodes | Edges | d | CC |
---|---|---|---|---|

Facebook [ |
40399 | 88234 | 8.5 | 0.11 |

Bright Kite [ |
58228 | 40399 | 8.9 | 0.8 |

Epinions [ |
75,877 | 405,739 | 10.7 | 0.14 |

We have implemented the clustering coefficient control mechanism by changing the value of probability, i.e., clustering control parameter

We herein define a network growth model that is completely based on the properties of self-organized networks.

Typically, highly clustered and scale-free networks are used. We considered the dependence and growth of networks that are similar to the small-world transition. This phenomenon was observed in many cases of static networks, especially when link rewiring to a regular grid is required. Hence, our study demonstrated a connection between the small-world and scale-free networks. Our proposed random walk model dynamically estimates the clustering coefficient and degree distribution in the network. The proposed random walk model considerably outperformed state-of-the-art methods. We tested our algorithm and concluded that our random walk model is helpful for network growth. Moreover, it is also highly efficient in terms of attaining the node degree and high clustering. Our model is beneficial for several network mining problems including extrapolation, sampling, and model testing. The path length was not discussed, although it is an important property of small-world networks. This will be addressed in future studies.

We thank our families and colleagues who provided us with moral support.