Scale-Free Network Topologies with Clustering Similar to Online Social Networks

Abstract

In this paper I propose a novel method to model real online social networks where the growing scale-free networks have tunable clustering coefficient independently of the average degree and the exponent of the degree distribution. Models based on purely preferential attachment are not able to describe high clustering coefficient of social networks. Beside the attractive popularity my model is based on the fact that if a person knows somebody, probably knows several individuals from his/her acquaintanceship as well. The topological properties of these complex systems were studied and it was found that in my networks the cliques are relevant independently of the system size as usual in social systems.

Social Network Limits Language Complexity

“…It would be ideal to also compare the common BA model with the transitivities present in the hierarchical network; however, a number of problems exist for this at present. First, the traditional BA model does not produce the requisite levels of transitivity present in observed social networks (Ravasz & Barab asi, 2003;Varga, 2015). Second, while modified versions of the BA model exist to try and make this property an adjustable parameter (Jin et al, 2001;Varga, 2015), as well as novel procedures to produce scale-free networks with tunable transitivity (Chakrabarti, Heath, & Ramakrishnan, 2017;Herrera & Zufiria, 2011), no method yet exists that accounts for the distribution of connection density in a way that mimics social networks and/or allows for manipulation of that density measure beyond a narrow range.…”

“…First, the traditional BA model does not produce the requisite levels of transitivity present in observed social networks (Ravasz & Barab asi, 2003;Varga, 2015). Second, while modified versions of the BA model exist to try and make this property an adjustable parameter (Jin et al, 2001;Varga, 2015), as well as novel procedures to produce scale-free networks with tunable transitivity (Chakrabarti, Heath, & Ramakrishnan, 2017;Herrera & Zufiria, 2011), no method yet exists that accounts for the distribution of connection density in a way that mimics social networks and/or allows for manipulation of that density measure beyond a narrow range. A key issue is that in large, scale-free human social networks, the local transitivity of an agent is inversely proportional to its number of connections, for example, to its degree (Soffer & Vazquez, 2005).…”

From the power law to extreme value mixture distributions

“…One particular class of discrete data for which the power law is often suitable is the degree distribution or related characteristics of networks. Examples include networks of links on the World-Wide Web (Barabási and Albert, 1999, Faloutsos et al, 1999, social networks (Lee, 2014, Lee and Oh, 2014, Varga, 2015, coauthorship/collaboration and citation networks (de Solla Price, 1976, Newman, 2001a,b, 2004, Thelwall and Wilson, 2014, Ji and Jin, 2016, Arroyo-Machado et al, 2020, retweet counts Bhamidi et al (2015), Mathews et al (2017). As an example, consider the citation network of a computer science conference, which corresponds to the top-right plots of Figures 1 and 2, and has been analysed by Lee et al (2019).…”

Social Network Limits Language Complexity

“…First, the traditional BA model does not produce the requisite levels of transitivity present in observed social networks (Ravasz and Barabási, 2003;Varga, 2015). Second, while M a n u s c r i p t modified versions of the BA model exist to try and make this property an adjustable parameter (Jin et al, 2001;Varga, 2015), as well as novel procedures to produce scale-free networks with tunable transitivity (Chakrabarti et al, 2017;Herrera and Zufiria, 2011), no method yet exists that accounts for the distribution of connection density in a way that mimics social networks, and/or allows for manipulation of that density measure beyond a narrow range. A key issue is that in large, scale-free human social networks, the local transitivity of an agent is inversely proportional to its number of connections, i.e.…”