Abstract
The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions. Various microscopic processes have been incorporated in these models, among them, node and edge addition, vertex fitness and the deletion of nodes and edges. The existing models, however, focus on specific combinations of these processes and parameterize them in a way that makes it difficult to elucidate the role of the individual elementary mechanisms. We therefore formulated and solved a model that incorporates the minimal processes governing network evolution. Some contribute to growth such as the formation of connections between existing pair of vertices, while others capture deletion; the removal of a node with its corresponding edges, or the removal of an edge between a pair of vertices. We distinguish between these elementary mechanisms, identifying their specific role on network evolution.
Highlights
The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions
While the preferential attachment model captures the qualitative features of network evolution, it is a minimal model with obvious limitations: (i) It predicts the value of the degree exponent to be c 5 3, whereas most real world networks have exponents in the range 2 # c # 4. (ii) It predicts a pure power law degree distribution, while real systems are characterized by small degree saturation and high-degree cutoffs. (iii) It ignores a number of elementary processes that play an important role in the evolution of many real networks, like the addition of internal links and node or link removal
When considered[24,25,26,27,28,30], this was studied in conjunction only with preferential attachment of new nodes, and the qualitative results were sound the predictions for the degree exponent c . 3 even in the presence of low deletion rates, was not in agreement with what is seen in real networks
Summary
The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions. (iii) It ignores a number of elementary processes that play an important role in the evolution of many real networks, like the addition of internal links and node or link removal To account for these limitations, a considerable amount of research has been conducted in the network science community, exploring a series of pertinent modifications to the original model, by changing the form of the attachment probability[11,12,13,14,15,16], incorporating effects such as ageing[17,18,19,20], fitness[21,22,23], and allowing for the simultaneous addition and deletion of edges and vertices[24,25,26,27,28,29], each leading to predictions that approximate better the degree distributions observed in real systems. Our primary goal is not necessarily to uncover new results ( we do present a series of new findings) but rather separate the ‘‘wheat from the chaff’’ untangling the results of previous work, putting in context and interpreting the role of the individual growth processes
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