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There are many networks in our daily lives; they surround us, interwoven like spider webs. Flight networks, metro networks, the Internet, food chain networks, social networks, financial networks, biological networks…They are everywhere! Networks represent relationships and interactions. Instead of focusing on a single individual, they focus on the relationships between individuals or groups.

 

Network Structure

Let us now focus on the structure of a network. A node is a single unit in a diagram or system; the link or connection between two nodes is called an edge. A network is composed of nodes and edges. It is a group of units that can but are not necessarily connected, as shown in Figure 1(a). Three or more nodes form a motif, as shown in Figure 1(b), while larger groups of nodes form a module, also called a community or a cluster, as shown in Figure 1(c). [1][2]

Figure 1. Network structure.

(a) Nodes and edges form a network. (b) Motif. (c) Module, community, or cluster.

 

Indicators for Network Evaluation

The most important indicator for network evaluation is the node degree, which is the number of edges connected to this node (regardless of the direction). A hub refers to a node with an abnormally high node degree, representing a key item in the network. The in-degree of a node refers to the number of edges that use this node as the target or where they end, and the out-degree of a node refers to the number of edges that use this node as the source or where they start (Figure 2). [1][2]

Figure 2. Network nodes’ node degree, in-degree, and out-degree.

Node 1 has a degree of 2, an in-degree of 2, and an out-degree of 1. Node 4 has a degree of 2, an in-degree of 1, and an out-degree of 2. Node 2 and node 3 have a degree of 1, an in-degree of 1, and an out-degree degree of 1.

 

Social Networks

Humans do not live in isolation but interact with each other, make connections, form a social circle, and eventually form a social network. In a social network, people with similar backgrounds form clusters, such as family, college classmates, club members, and church friends. A collaboration network is also a type of social network, in which the nodes are scholars and the edges are their publications, such that the collaborative relationship between the scholars can be examined. The Nature Index, provided by the renowned international journal Nature, can track the affiliation relationships among high-quality scientific articles. From October 2020 to September 2021, the top five countries in the Nature Index are the United States, China, Germany, the United Kingdom, and Japan. Through the collaboration networks of these top five countries, one can examine the academic partnerships among these countries’ high-quality scientific articles and discover that scholars from the United States and China have collaborated closely.[3]

 

Core Hub of a Social Network

The elite family network in 15^th-century Florence is also an interesting example of a social network, in which the nodes represent families and the edges represent relationships such as business and marriage. It is found from the network that the Medici family was not only the center of the network structure but also a key liaison. Some families that had no direct relationships with each other needed the Medici family to connect them, as shown in Figure 3. Because the Medici family was situated in an important network position, it played an important mediator role in politics, as well as a key intermediary in business. This is why the Medici were called the “Godfathers of the Renaissance.”[4][5][6]

Figure 3. Elite family network of Florence. The nodes represent the various elite families in Florence; the edges represent business or marital relationships. 

   

Interpersonal Alienation and Homophily in Social Network

In the mid-1900s, according to the data from Add Health, a longitudinal adolescent-to-adult health study in the United States, the friendship network of American high school students showed that those who identified as black and those who identified as white were alienated from each other. People with the same self-identified skin colors were closer to each other than people with different skin colors. The chance of two people of the same race becoming friends is more than 15 times higher than that of a black-and-white pair. If the connections are further limited to only “close friends” who engaged in at least three activities together each week and are in close contact with each other, then this type of relationship between black and white individuals was almost non-existent, and the interpersonal alienation was even more obvious. It was evident that people tend to interact with those who are similar to them in terms of race, age, occupation, education level, etc. This phenomenon is called homophily, a term proposed in 1954, with homo meaning “same” and phily meaning “inclination or fondness.”[4]

 

Social Network, Small World, and Six Degrees of Separation

Globalization has made the social network between people closer. Today's world is shrinking. The shortest path between any two people in the world has become quite short, hence the “six degrees of separation” theory has been developed. Six degrees of separation means that you are connected with any random person in the world through “friends of friends,” and you only need to make six or fewer such connections (Figure 4). As early as 1929, the Hungarian writer Frigyes Karinthy coined the term “small world.” Later, John Guare's play “Six Degrees of Separation” made this concept even more well-known. [4]

Figure 4. Six degrees of separation.

You can be connected to any random person in the world through just six or fewer connections.

 

In 1967, Harvard social psychologist Stanley Milgram performed a chain letter experiment, also known as the small-world experiment. Each subject was instructed to mail a document to a designated recipient with a known name, the town of residence, and other background information. The subjects were not allowed to contact the recipients they did not know; rather, they had to mail the documents to an acquaintance of theirs who were most likely to know the recipients. If you received the letter, you should mail the document to the next acquaintance who may know the final recipient. Through successive forwarding of the document, it was hoped that the letter would finally be delivered to the designated recipient. For the intermediate people who received the letters, they just knew that they received them from an acquaintance, yet the rate of forwarding these letters to the final designated recipients was surprisingly high. Among the 160 documents, 44 were successfully delivered—a success rate as high as 27.5%. In addition, it is worth noting that in successful cases, the letters only needed to be forwarded five times on average to successfully reach the specific person. Even though the experiment had its limitations, this phenomenon attracted much attention in academia. [4][7]

As times go by, the social media platform Facebook has become widely used, and the phenomenon of the small world can also be found in the friend relationships on Facebook. Suppose we have a typical Facebook user, Joe, who has an average of 200 Facebook friends. Now, if we look at the next circle of friends just outside Joe’s circle, we see that each of Joe’s Facebook friends also has an average of 200 Facebook friends. While Joe does not know any of these “friends of friends,” he can reach 200 × 200 = 40,000 Facebook users. Then, if we expand the circle of friends further, Joe can reach 8 million people three steps away and 1.6 billion people four steps away![4]

The concept of the small world and the six degrees of separation theory are not that far from us. At the end of 2019, the original COVID-19 epidemic was only happening in China, but due to the normal international round-trip flights and the lack of screening in various countries, the epidemic spread rapidly to the rest of the world in just a few months. It is evident that networks have a huge impact on life and can even set off a huge chain reaction all over the world.

Networks are ubiquitous and closely related to our lives, and the analysis and application of networks are also quite extensive. They can be combined with artificial intelligence to create new things and ideas. For example, social networks can be used for epidemic monitoring and control, fake news detection, recommendation systems, and even school-dropout prevention. In addition, financial networks can be used for risk control, and biomolecules can also form a biological network for the discussion of disease mechanisms and the development of drugs. For details, please tune in to the next episode.

 

 

References

 

Written by Dr. Chih-Hsun Wu , Researcher, the Artificial Intelligence and E-Learning Center, National Chengchi University