| Abstract |
Network motifs represent local subgraphs, such as dyads, triads, and tetrads, that occur frequently in networks. The biological and physical sciences document multiple instances in which motifs appear in graphs that provide insight into the structure and processes of these networks. Yet, little work has studied motifs within social graphs. In this research, we examine the prevalence of dyad, triad, and tetrad motifs among six types of social interactions, including friendship, advice seeking, email communication, twitter messages, terrorist ties, and legislative cosponsorship. We use four networks of each type, for a total sample of 24 social networks. One contribution of our work is the use of the UMAN distribution, which controls for the number of mutual, asymmetric, and null dyads, when determining the significance profile of triad and tetrad frequencies. We argue that this distributional control has advantages over other controls used in previous research, because mutual dyads are extremely common in social graphs. We find important commonalities among the six types of networks in our sample, suggesting that there are specific motifs that characterize multiple genres of social network data. Reciprocity of directed ties occurs more frequently than expected by chance in all of our graphs. Completely connected triads and tetrads (i.e., four-node subgraphs) also occur more often than expected, which highlights the tendency of actors to form clusters of ties. We also identify motifs that reflect patterns of hierarchy. In addition, one intriguing tetrad motif points to the bridging of gaps, or “structural holes,” between nodes and implies that the networks in our sample are made of both strong ties that lead to clustering, and weaker ones that result in bridging. Furthermore, we find that certain motifs are specific to some genres of social networks, but not others. For instance, a common motif among biological networks, known as a “bifan” tetrad (i.e., nodes i and j each send non-reciprocated ties to nodes k and l), is more likely to occur among the Twitter, friendship, and advice networks in our sample, but not in others. |