THESIS
2019
xi, 108 pages : illustrations ; 30 cm
Abstract
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...[
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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.
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