Related papers: Cluster Growth in a Growing Tree Network

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…

Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…

We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive…

Real-world networks are rarely static. Recently, there has been increasing interest in both network growth and network densification, in which the number of edges scales superlinearly with the number of nodes. Less studied but equally…

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…

We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…

The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…

We study the evolution of percolation with freezing. Specifically, we consider cluster formation via two competing processes: irreversible aggregation and freezing. We find that when the freezing rate exceeds a certain threshold, the…

We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no…

Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…

We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…