We present new network formation models, which are featured on the search process of edges instead of nodes. In the models, new nodes arrive sequentially and create connections with old nodes. Accordingly, the network forms and grows. There are two steps for a new node to search and create connections: 1. a new node finds a link/edge and both end-nodes, then the new node may create connections with the end-nodes; 2. the new node finds the neighbors of the tail-node, and tries to create connections with the tail-node’s neighborhood. Practically, these network formation models capture the process that an individual learns something and tries to construct cooperations with the authors. For example, in a co-authorship network, a scholar reads a paper and seeks to collaborate with t...[ Read more ]

We present new network formation models, which are featured on the search process of edges instead of nodes. In the models, new nodes arrive sequentially and create connections with old nodes. Accordingly, the network forms and grows. There are two steps for a new node to search and create connections: 1. a new node finds a link/edge and both end-nodes, then the new node may create connections with the end-nodes; 2. the new node finds the neighbors of the tail-node, and tries to create connections with the tail-node’s neighborhood. Practically, these network formation models capture the process that an individual learns something and tries to construct cooperations with the authors. For example, in a co-authorship network, a scholar reads a paper and seeks to collaborate with the authors of this paper. In our models, there are two tiers of collaborations for each node. That is a node can reach one step further beyond initial connections. By examining the proportion of “the friends of my friends are also my friends”, we can obtain the closeness of the relation in this network.

The contributions are as follows: 1. In our models, a new node searches links rather than counts degree of nodes. “Searching” is more applicable than “counting.” The reason is that, for example, a scholar reads another scholar’s paper rather than counts another scholar’s papers before constructing a collaboration. That is the behaviors of learning in a social network is captured by the search process. Moreover, mathematical modeling regarding “searching” is more complicated than “counting” because “counting” does not need to label links/edges, while “searching” needs to label links/edges. Furthermore, it is applicable for the models to describe social networks where people have cooperations, for example, co-authorship network, film actors network, and musicians network. 2. Edge-based models capture the heterogeneity of the degree of nodes. That is, we calculate the variance of out-degree beyond the mean-field approximation. 3. Numeric simulations are presented to verify the theoretical results of the model. 4. The dataset of co-authorship networks in economics is analyzed to illustrate the applicability of the model. From the data analytics, we show that our models perform better than previous works.