Dynamic motifs in socio-economic networks

Socio-economic networks are of central importance in economic life. We develop a method of identifying and studying motifs in socio-economic networks by focusing on “dynamic motifs,” i.e., evolutionary connection patterns that, because of “node acquaintances” in the network, occur much more frequently than random patterns. We examine two evolving bi-partite networks: i) the world-wide commercial ship chartering market and ii) the ship build-to-order market. We find similar dynamic motifs in both bipartite networks, even though they describe different economic activities. We also find that “influence” and “persistence” are strong factors in the interaction behavior of organizations. When two companies are doing business with the same customer, it is highly probable that another customer who currently only has business relationship with one of these two companies, will become customer of the second in the future. This is the effect of influence. Persistence means that companies with close business ties to customers tend to maintain their relationships over a long period of time. Copyright c ⃝ EPLA, 2014 Introduction. – Many complex physical, biological, and social systems can be modeled and better understood as complex networks [1–11]. Socio-economic research is a multidisciplinary research area in which relationships between economic activities and their social environment are used to constitute socio-economic networks. Understanding patterns of economic organization interactions is essential if we are to uncover the mechanism and the structure of the socio-economic environment [12–17]. Network motif analysis is a sub-graph mining method proposed by Milo et al. [18]. Motifs are small (usually from three to seven nodes in size) connected sub-graphs within a given structure that appear in the network more frequently than they would if the network were completely random. This idea was first presented in 2002 by Uri Alon and his group, who discovered network motifs in the gene regulation network of the bacteria E. coli and in a large number of natural networks [18–20]. Following their seminal work, many studies have been conducted on this subject. Network motifs have been found in systems such as biological networks [19,21], electronic circuit networks [22], transport networks [23], and individual online affiliation networks [24]. Although some researchers have used network motifs to understand how social relationships influence individual interactions [25], little research has examined the impact of the socio-economic network itself on interactions among the organizations of the network [26]. To date most research has focused on static network motifs that are either a single-time snapshot of a phenomenon being investigated or an aggregate view over time [27]. Because most complex phenomena are time-varying, researchers are beginning to consider dynamic networks that evolve over time, such as how the network structure evolves in time with changes across physiological states [28–30]; however there is less research on time evolution of real networks in economic systems. Both network topology and its time evolution must be considered if we are to understand the dynamics of a complex network. Our approach to this problem is to develop a method that allows us to analyze statistically the evolution of socio-economic motifs. We define dynamic network motifs as statistically significant sub-graph patterns that evolve in a network. By tracking the occurrence of dynamic motifs in a network that models organizational socio-economic interactions, we can observe the evolution of local configurations. Using this model we can then evaluate how a socio-economic network influences a company’s decisions.