Tore Opsahl

Thesis: 4.1 Network growth mechanisms

A number of mechanisms have been thought to affect nodes’ decision-making. First, as mentioned in Chapter 2, there tend to be many more triangles of nodes in networks than one would expect by chance (Davis, 1970; Erdos and Renyi, 1960; Heider, 1946;Rapaport, 1953). This might be the result of individuals’ desire to maintain balance among ties with others (“my friends’ friends are my friends”; Hallinan, 1974; Heider, 1946).. Another explanation refers to third-part referral (Davis, 1970; Holland and Leinhardt, 1971). A person’s social circles are likely to overlap through social occasions, during which, a person might introduce people from the different circles to each other. In the literature, the mechanism underpinning the creation of triangles is known as triadic closure (Burt, 2005; Heider, 1946; Holland and Leinhardt, 1971).

Second, a number of empirical studies have shown that ties are not equally distributed across nodes (Barabasi and Albert, 1999; Barabasi et al., 2002; Dorogovtsev and Mendes, 2003; Jeong et al., 2003). The majority of nodes attract only few ties, whereas there are a select minority of nodes that receive a disproportionately large number of ties (Barabasi and Albert, 1999). A possible explanation for this type of skewed distribution is that popularity is attractive (Dorogovtsev and Mendes, 2003). In other words, a virtuous effect occurs for the “popular” nodes whereby they receive relatively more ties than others as the network evolves. This mechanism has been independently rediscovered several times in different areas of research. Simon (1955) called this mechanism the “Gibrat” principle after French economist Robert Gibrat (1904-1980). Gibrat argued that the proportional change in the firm size is the same for all firms in an industry. This implies that if one firm doubles its size in 10 years, all other firms will also double in size. Thus, the biggest firms will become bigger and bigger relative to all the others. Merton (1968) referred to this concept as the “Matthew effect”, after the first part of the biblical edict, “For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him.” (Matthew, 25:29). More recently, Barabasi and Albert (1999) coined the term “preferential attachment”, which states that nodes preferential “attach” or create ties with high degree nodes. In particular, they showed that a high number of hyper-links on the Internet point towards a small number of pages.

Third, in a directed network, two directed ties can exist between two nodes in a dyad – one in each direction. It has been found that in most networks, there are more dyads with two directed ties than randomly expected (Gouldner, 1960; Holland and Leinhardt, 1981; Plickert et al., 2007; Wasserman and Faust, 1994). In fact, the vast majority of dyads in the airport network studied in Chapter 3 have either two or no directed ties. Extremely few dyads consist of a single directed tie (Barrat et al., 2004; Guimera et al., 2005). The mechanism that increases the likelihood of creating a second directed tie in a dyad is referred to as reciprocity (Gouldner, 1960; Holland and Leinhardt, 1981; Plickert et al., 2007).

Fourth, socially similar people have been found to create ties with each other to a greater extent than randomly expected (Lazarsfeld and Merton, 1954; McPherson et al., 2001). It has been argued that this is due to the fact that similarity generates a baseline level of interpersonal attraction (McPherson et al., 2001). In addition, it has been shown that similarity bring about more stable and stronger ties between people than randomly expected (Hallinan and Kubitschek, 1988; Hinds et al., 2000; Reagans and McEvily, 2003; Lazarsfeld and Merton, 1954). Moreover, individuals are likely to participate in joint activities with others who have similar interests as they receive validation of their attitudes and beliefs (Aboud and Mendelson, 1996). The mechanism that is responsible for the generation of ties among similar nodes has been named homophily.

Fifth, another mechanism that is thought to affect tie generation is focus constraint (Feld, 1981; Kalmijn and Flap, 2001). This mechanism is defined as the increased likelihood of a tie being present among people that share activities, roles, social positions, and geographical location. For example, a group of people working in the same office are more likely to interact than simply a group of people in geographically distance places.

The outcomes of measures designed to test these mechanisms individually can be biased as only a single feature of the network structure is described. It could be the case that triadic closure and homophily affected the likelihood of a tie in a network. If so, an observed triangle formed among three similar people can be attributed to both triadic closure and homophily, and it would be difficult to assess whether, and the extent to which, the triangle was formed due to either of these mechanisms.