Abstract
Many realworld networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, highdegree nodes tend to be linked with lowdegree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an efficient and exact method to construct and sample graphs with a specified jointdegree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is O(NM) where N is the number of nodes and M is the number of edges.
Original language  English 

Article number  083052 
Journal  New Journal of Physics 
Volume  17 
DOIs  
Publication status  Published  31 Aug 2015 
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Charo del Genio
 Research Centre for Fluid and Complex Systems  Assistant Professor Academic
Person: Teaching and Research