Related papers: Eigenvalue Preferential Attachment Networks A Dand…
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…
We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
Preferential attachment models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. One of the things they lack, however, is higher-order network…
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…
We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution,…
The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the…