Related papers: Spreading on a complex network avoiding certain mo…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
Many real-world complex networks actually have a bipartite nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad-hoc tools have been…
This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a…
We study scale free simple graphs with an exponent of the degree distribution $\gamma$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special…
It is a mainstream idea that scale-free network would be fragile under the selective attacks. Internet is a typical scale-free network in the real world, but it never collapses under the selective attacks of computer viruses and hackers.…
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…
Network sampling is a crucial technique for analyzing large or partially observable networks. However, the effectiveness of different sampling methods can vary significantly depending on the context. In this study, we empirically compare…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…