Mixing properties of growing networks and Simpson's paradox.

The mixing properties of networks are usually inferred by comparing the degree of a node with the average degree of its neighbors. This kind of analysis often leads to incorrect conclusions: Assortative patterns may appear reversed by a mechanism known as Simpson's paradox. We prove this fact by analytical calculations and simulations on three classes of growing networks based on preferential attachment and fitness, where the disassortative behavior observed is a spurious effect. Our results give a crucial contribution to the debate about the origin of disassortative mixing, since networks previously classified as disassortative reveal instead assortative behavior to a careful analysis.

[1]  E. H. Simpson,et al.  The Interpretation of Interaction in Contingency Tables , 1951 .

[2]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[3]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Ginestra Bianconi,et al.  Competition and multiscaling in evolving networks , 2001 .

[5]  S. Julious,et al.  Confounding and Simpson's paradox , 1994, BMJ.

[6]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[7]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[8]  Christopher R. Myers,et al.  Software systems as complex networks: structure, function, and evolvability of software collaboration graphs , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  R. Pastor-Satorras,et al.  Class of correlated random networks with hidden variables. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

[11]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[12]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[13]  Alessandro Vespignani,et al.  Traffic-driven model of the World Wide Web graph , 2004, WAW.

[14]  Alain Barrat,et al.  Rate equation approach for correlations in growing network models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Y. Moreno,et al.  Resilience to damage of graphs with degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Guido Caldarelli,et al.  Loops structure of the Internet at the autonomous system level. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  G. Caldarelli,et al.  Quantitative description and modeling of real networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[19]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.