Related papers: Emergence of multiscaling in heterogeneous complex…
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…
We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the…
Preferential attachment is the most popular explanation for the emergence of scaling behavior in the World Wide Web, but this explanation has been challenged by the global information hypothesis, the existence of linear preference and the…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
This paper presents a tighter bound on the degree distribution of arbitrary P\'{o}lya urn graph processes, proving that the proportion of vertices with degree $d$ obeys a power-law distribution $P(d) \propto d^{-\gamma}$ for $d \leq…
We investigate the higher-order connectivity of scale-free networks using algebraic topology. We model scale-free networks as preferential attachment graphs, and we study the algebraic-topological properties of their clique complexes. We…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…