Migration in a Small World: A Network Approach to Modeling Immigration Processes

Existing theories of migration either focus on micro- or macroscopic behavior of populations; that is, either the average behavior of entire population is modeled directly, or decisions of individuals are modeled directly. In this work, we seek to bridge these two perspectives by modeling individual agents decisions to migrate while accounting for the social network structure that binds individuals into a population. Pecuniary considerations combined with the decisions of peers are the primary elements of the model, being the main driving forces of migration. People of the home country are modeled as nodes on a small-world network. A dichotomous state is associated with each node, indicating whether it emigrates to the destination country or it stays in the home country. We characterize the emigration rate in terms of the relative welfare and population of the home and destination countries. The time evolution and the steady-state fraction of emigrants are also derived

Degree Correlation in Scale-Free Graphs

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination preferential attachment growth model, where incoming nodes at each timestep attach to $\beta$ existing nodes, selected by degree-proportional probabilities. By the conditional degree distribution $p(\ell| k)$, we mean the degree distribution of nodes that are connected to a node of degree $k$. By the joint degree distribution $p(k,\ell)$, we mean the proportion of links that connect nodes of degrees $k$ and $\ell$. In addition to this growth model, we consider the shifted-linear preferential growth model and solve for the same quantities, as well as a closed form expression for its steady-state degree distribution