Related papers: From Scale-free to Erdos-Renyi Networks
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Understanding how individual learning behavior and structural dynamics interact is essential to modeling emergent phenomena in socioeconomic networks. While bounded rationality and network adaptation have been widely studied, the role of…
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…
Temporal gene expression data (Wen, et. al.) was analyzed using the recently introduced inverse modeling technique of Embedded Complex Logistic Maps (ECLM). Preliminary results indicate scale-free structure in the gene regulatory network…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…
The problem of real-time processing is one of the most challenging current issues in computer sciences. Because of the large amount of data to be treated in a limited period of time, parallel and distributed systems are required, whose…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we…
With a simple attack and repair evolution model, we investigate and compare the stability of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to describe the…
Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models for…
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices $x,y\in\mathbb{Z}^d$ are linked by an edge with probability depending on i.i.d.\ vertex weights and the Euclidean distance…
This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider {\em ad hoc} (i.e., nodes can leave the network unannounced,…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a…
Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…
Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…
This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…