There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we first empirically study preferential linking phenomena in an evolving online social network, find and validate the linear preference. We propose an analyzable model which captures the real growth process of the network and reveals the underlying mechanism dominating its evolution. Furthermore based on preferential linking we propose a generalized model reproducing the evolution of online social networks, present unified analytical results describing network characteristics for 27 preference scenarios, and explore the relation between preferential linking mechanism and network features. We find that within the framework of preferential linking analytical degree distributions can only be the combinations of finite kinds of functions which are related to rational, logarithmic and inverse tangent functions, and extremely complex network structure will emerge even for very simple sublinear preferential linking. This work not only provides a verifiable origin for the emergence of various network characteristics in social networks, but bridges the micro individuals' behaviors and the global organization of social networks.
Bitcoin and Ethereum transactions present one of the largest real-world complex networks that are publicly available for study, including a detailed picture of their time evolution. As such, they have received a considerable amount of attention from the network science community, beside analysis from an economic or cryptography perspective. Among these studies, in an analysis on the early instance of the Bitcoin network, we have shown the clear presence of the preferential attachment, or "rich-get-richer" phenomenon. Now, we revisit this question, using a recent version of the Bitcoin network …
In this paper, we analyze assortativity of preferential attachment models. We deal with a wide class of preferential attachment models (PA-class). It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global and the average local clustering coefficients were analyzed. We expand these results by analyzing the assortativity property of the PA-class of models. Namely, we analyze the behavior of $d_{nn}(d)$ which is the average degree of a neighbor of a vertex of degree $d$.
Network Inequality through Preferential Attachment, Triadic Closure, and Homophily
Complexity Science Hub（复杂性科学中心）；Department of Network and Data Science, Central European University（中欧大学网络与数据科学系）；Graz University of Technology（格拉茨工业大学）；Grupo de Sistemas Complejos, ETS de Arquitectura de Madrid, Universidad Politécnica de Madrid（马德里理工大学马德里建筑高等技术学院复杂系统小组）；Faculty of Engineering, Free University of Bozen-Bolzano（博尔扎诺-博岑自由大学工程学院）；Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico（里斯本高等理工学院计算与随机数学中心）
The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects, not aging and decline. Recent aging models are complex and heavily parameterized; most involve estimating 1-3 parameters per node. These parameters are intrinsic: they explain decline in terms of events in the past of the same node, and do not explain, using the network, where the linking attention might go instead. We argue that traditional characterizatio…
This paper expands the degree-based consideration of the preferential attachment growth process and applies five different connectivity criteria (node degree, clustering coefficient, betweenness centrality, closeness centrality, and eigenvector centrality) to define the development of new links in the networks. Based on statistical inference, the analysis shows that all the available control attributes are capable generating SF networks, that the proposed generalized preferential attachment growth process produces networks of statistically different topologies, under different control-attribut…
The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment-like network growth mechanism governed by both node degrees and `qualities'. We introduce measures to quantify paradoxes, and contrast the results obtained in our model to those obtained for an uncorrel…
In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabasi-Albert (BA) differential equation, ge…
In this paper, I study epidemic diffusion in a generalized spatial SEIRD model, where individuals are initially connected in a social or geographical network. As the virus spreads in the network, the structure of interactions between people may endogenously change over time, due to quarantining measures and/or spatial-distancing policies. I explore via simulations the dynamic properties of the co-evolutionary process dynamically linking disease diffusion and network properties. Results suggest that, in order to predict how epidemic phenomena evolve in networked populations, it is not enough to…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient on dynamical processes taking place on networks, some authors have focused on the construction of graphs with tunable clustering coefficients. These constructions are usually realized through a stochastic process, either by growing a network through the preferential attachment procedure, or by applying a random rewiring process. In contrast, we consider her…
GEMINI: Generalized Ensnarlment Measure from Incomplete-linkage of Network-network Interactions
Max-Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；TU Dresden（德累斯顿工业大学）
