Abstract
In this paper we present a generalization of the classical configuration model. Like the classical configuration model, the generalized configuration model allows users to specify an arbitrary degree distribution. In our generalized configuration model, we partition the stubs in the configuration model into b blocks of equal sizes and choose a permutation function h for these blocks. In each block, we randomly designate a number proportional to q of stubs as type 1 stubs, where q is a parameter in the range [0,1]. Other stubs are designated as type 2 stubs. To construct a network, randomly select an unconnected stub. Suppose that this stub is in block i. If it is a type 1 stub, connect this stub to a randomly selected unconnected type 1 stub in block h(i). If it is a type 2 stub, connect it to a randomly selected unconnected type 2 stub. We repeat this process until all stubs are connected. Under an assumption, we derive a closed form for the joint degree distribution of two random neighboring vertices in the constructed graph. Based on this joint degree distribution, we show that the Pearson degree correlation function is linear in q for any fixed b. By properly choosing h, we show that our construction algorithm can create assortative networks as well as disassortative networks. We present a percolation analysis of this model. We verify our results by extensive computer simulations.
Highlights
Recent advances in the study of networks that arise in field of computer communications, social interactions, biology, economics, information systems, etc., indicate that these seemingly widely different networks possess a few common properties
In “Assortativity anddisassortativity” section, we show that the Pearson degree correlation function of two neighboring vertices is linear
In this paper we propose an extension of the classical configuration model
Summary
Recent advances in the study of networks that arise in field of computer communications, social interactions, biology, economics, information systems, etc., indicate that these seemingly widely different networks possess a few common properties. Our method allows us to derive a closed form for the Pearson degree correlation function for two random neighboring vertices under an assumption. In “Joint distribution of degrees” section we derive a closed form for the joint degree distribution of two randomly selected neighboring vertices from a network constructed by the algorithm in “Construction of a random network” section.
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