Structural Bounds on the Dyadic Effect

In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to measure how much the assigned characteristic affects the network topology. All possible configurations can be represented in a phase diagram lying in a two-dimensional space that represents the feasible region of the dyadic effect, which is bound by two upper bounds on dyadicity and heterophilicity. Using some network's structural arguments, we are able to improve such upper bounds and introduce two new lower bounds, providing a reduction of the feasible region of the dyadic effect as well as constraining dyadicity and heterophilicity within a specific range. Some computational experiences show the bounds' effectiveness and their usefulness with regards to different classes of networks.

[1]  A. Giuliani,et al.  Protein contact networks: an emerging paradigm in chemistry. , 2013, Chemical reviews.

[2]  Duncan J. Watts,et al.  The Structure and Dynamics of Networks: (Princeton Studies in Complexity) , 2006 .

[3]  M. McPherson,et al.  BIRDS OF A FEATHER: Homophily , 2001 .

[4]  Xia Li,et al.  The expanded human disease network combining protein–protein interaction information , 2011, European Journal of Human Genetics.

[5]  Vinko Zlatic,et al.  Robustness and assortativity for diffusion-like processes in scale-free networks , 2011, ArXiv.

[6]  T. Jiang,et al.  Modularity in the genetic disease‐phenotype network , 2008, FEBS letters.

[7]  P. Tiberto,et al.  Magnetic properties of jet-printer inks containing dispersed magnetite nanoparticles , 2013 .

[8]  Ernesto Estrada,et al.  Combinatorial study of degree assortativity in networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  T. Neumann.  Computers And Intractability A Guide To The Theory Of Np Completeness , 2016 .

[10]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[11]  P. Pin,et al.  Assessing the relevance of node features for network structure , 2008, Proceedings of the National Academy of Sciences.

[12]  Stojan Trajanovski,et al.  Random line graphs and a linear law for assortativity. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[14]  THE EUROPEAN PHYSICAL JOURNAL B Scale-free homophilic network , 2013 .

[15]  Harry Eugene Stanley,et al.  Assortativity Decreases the Robustness of Interdependent Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  R. Alba.  A graph‐theoretic definition of a sociometric clique† , 1973 .

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

[18]  S. Hakimi.  On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I , 1962 .

[19]  M. M. Meyer,et al.  Statistical Analysis of Multiple Sociometric Relations. , 1985 .

[20]  Giovanna Ferraro,et al.  Revealing correlations between structure and innovation attitude in inter-organisational innovation networks , 2015 .

[21]  Matteo Cinelli,et al.  Some Insights into the Relevance of Nodes’ Characteristics in Complex Network Structures , 2016 .

[22]  William B. Langdon,et al.  Performance of genetic programming optimised Bowtie2 on genome comparison and analytic testing (GCAT) benchmarks , 2015, BioData Mining.

[23]  M. E. J. Newman,et al.  Mixing patterns in networks: Empirical results and models , 2002 .

[24]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[25]  Giovanna Ferraro,et al.  Organizing Collaboration in Inter-Organizational Innovation Networks, from Orchestration to Choreography , 2015 .

[26]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[27]  O. Sporns,et al.  High-cost, high-capacity backbone for global brain communication , 2012, Proceedings of the National Academy of Sciences.

[28]  Giovanna Ferraro,et al.  On the influence of nodes' characteristic in inter-organisational innovation networks structure , 2016 .

[29]  Alessandro Vespignani,et al.  Detecting rich-club ordering in complex networks , 2006, physics/0602134.

[30]  Albert-László Barabási,et al.  Distribution of node characteristics in complex networks , 2007, Proceedings of the National Academy of Sciences.

[31]  Piet Van Mieghem,et al.  Assortativity in complex networks , 2015, J. Complex Networks.

[32]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[33]  Albert-Lszl Barabsi,et al.  Network Science , 2016, Encyclopedia of Big Data.

[34]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[35]  L. R. Silva,et al.  Scale-free homophilic network , 2013 .

[36]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.

[37]  Ting Hu,et al.  Functional dyadicity and heterophilicity of gene-gene interactions in statistical epistasis networks , 2015, BioData Mining.

[38]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Hyunju Kim,et al.  Degree-based graph construction , 2009, 0905.4892.

[40]  F. Harary,et al.  The cohesiveness of blocks in social networks: Node connectivity and conditional density , 2001 .

[41]  Jeffrey Q. Jiang,et al.  Towards Prediction and Prioritization of disease genes by the modularity of human phenome-genome assembled network , 2010, J. Integr. Bioinform..

[42]  Thilo Gross,et al.  All scale-free networks are sparse. , 2011, Physical review letters.