Dynamics of node influence in network growth models

We examine the dynamics for the average degree of a node’s neighbors in complex networks. It is a Markov stochastic process, and at each moment of time, this quantity takes on its values in accordance with some probability distribution. We are interested in some characteristics of this distribution: its expectation and its variance, as well as its coefficient of variation. First, we look at several real communities to understand how these values change over time in social networks. The empirical analysis of the behavior of these quantities for real networks shows that the coefficient of variation remains at high level as the network grows. This means that the standard deviation and the mean degree of the neighbors are comparable. Then, we examine the evolution of these three quantities over time for networks obtained as simulations of one of the well-known varieties of the Barabási–Albert model, the growth model with nonlinear preferential attachment (NPA) and a fixed number of attached links at each iteration. We analytically show that the coefficient of variation for the average degree of a node’s neighbors tends to zero in such networks (albeit very slowly). Thus, we establish that the behavior of the average degree of neighbors in Barabási–Albert networks differs from its behavior in real networks. In this regard, we propose a model based on the NPA mechanism with the rule of random number of edges added at each iteration in which the dynamics of the average degree of neighbors is comparable to its dynamics in real networks.

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Emergence of dense scale-free networks and simplicial complexes by random degree-copying

Esquivel-Gómez,

Barajas-Ramírez

2023

Journal of Complex Networks

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Many real-world networks exhibit dense and scale-free properties, that is, the amount of connections among the nodes is large and the degree distribution follows a power-law P(k)∼k−γ. In particular, for dense networks γ∈(1,2]. In the literature, numerous network growth models have been proposed with the aim to reproduce structural properties of these networks. However, most of them are not capable of generating dense networks and power-laws with exponents in the correct range of values. In this research, we provide a new network growth model that enables the construction of networks with degree distributions following a power law with exponents ranging from one to an arbitrary large number. In our model, the growth of the network is made using the well-known Barabási–Albert model, that is, by nodes and links addition and preferential attachment. The amount of connections with which each node is born, can be fixed or depending of the network structure incorporating a random degree-copying mechanism. Our results indicate that if degree-copying mechanism is applied most of the time, then the resulting degree distribution has an exponent tending to one. Also, we show that the resulting networks become denser as γ→1, in consequence their clustering coefficient increases and network diameter decreases. In addition, we study the emergence of simplicial complexes on the resulting networks, finding that largest simplicial dimension appears as γ decreases.

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Dynamics of node influence in network growth models

Cited by 4 publications

References 33 publications

Measuring user influence in real-time on twitter using behavioural features

Measuring user influence in real-time on twitter using behavioural features

Measuring the variability of local characteristics in complex networks: Empirical and analytical analysis

Emergence of dense scale-free networks and simplicial complexes by random degree-copying

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