Cture of numerous realworld networks creates conditions for the 'majority illusionCture of lots of realworld

March 5, 2019

Cture of numerous realworld networks creates conditions for the “majority illusion
Cture of lots of realworld networks creates situations for the “majority illusion” paradox.Components and MethodsWe utilised the configuration model [32, 33], as implemented by the SNAP library (https:snap. stanford.edudata) to create a scalefree network using a specified degree sequence. We generated a degree sequence from a power law from the form p(k)k. Here, pk would be the fraction of nodes that have k halfedges. The configuration model proceeded by linking a pair of randomly selected halfedges to type an edge. The linking procedure was repeated until all halfedges happen to be utilized up or there were no a lot more approaches to form an edge. To create ErdsR yitype networks, we started with N 0,000 nodes and linked pairs at random with some fixed probability. These probabilities have been chosen to generate typical degree similar for the average degree of your scalefree networks.PLOS One DOI:0.37journal.pone.04767 February 7,three Majority IllusionTable . Network properties. Size of networks studied in this paper, together with their average degree hki and degree assortativity coefficient rkk. network HepTh Reactome Digg Enron Twitter Political blogs nodes 9,877 6,327 27,567 36,692 23,025 ,490 edges 25,998 47,547 75,892 367,662 336,262 9,090 hki 5.26 46.64 two.76 20.04 29.2 25.62 rkk 0.2679 0.249 0.660 0.08 0.375 0.doi:0.37journal.pone.04767.tThe statistics of realworld networks we studied, which includes the collaboration network of higher power physicist (HepTh), Human protein rotein interactions network from Reactome project (http:reactome.orgpagesdownloaddata), Digg follower graph (DOI:0.6084 m9.figshare.2062467), Enron email network (http:cs.cmu.eduenron), Twitter user voting graph [34], and a network of political blogs (http:PD150606 site wwwpersonal.umich.edumejn netdata) are summarized in Table .ResultsA network’s structure is partly specified by its degree distribution p(k), which provides the probability that a randomly selected node in an undirected network has k neighbors (i.e degree k). This quantity also impacts the probability that a randomly selected edge is connected to a node of degree k, otherwise known as neighbor degree distribution q(k). Since highdegree PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/23139739 nodes have far more edges, they may be overrepresented in the neighbor degree distribution by a element proportional to their degree; hence, q(k) kp(k)hki, exactly where hki could be the average node degree. Networks typically have structure beyond that specified by their degree distribution: as an example, nodes could preferentially hyperlink to other people with a comparable (or pretty different) degree. Such degree correlation is captured by the joint degree distribution e(k, k0 ), the probability to find nodes of degrees k and k0 at either end of a randomly selected edge in an undirected network [35]. This quantity obeys normalization circumstances kk0 e(k, k0 ) and k0 e(k, k0 ) q(k). Globally, degree correlation in an undirected network is quantified by the assortativity coefficient, that is basically the Pearson correlation between degrees of connected nodes: ” ! X X 0 2 0 0 0 0 kk ; k q two kk e ; k hkiq : r kk 2 sq k;k0 sq k;k0 P P 2 Right here, s2 k k2 q k kq . In assortative networks (rkk 0), nodes have a tendency q link to equivalent nodes, e.g highdegree nodes to other highdegree nodes. In disassortative networks (rkk 0), alternatively, they prefer to hyperlink to dissimilar nodes. A star composed of a central hub and nodes linked only towards the hub is an instance of a disassortative network. We can use Newman’s edge rewiring procedure [35] to modify a network’s degree assort.