Related papers: Growing network with j-redirection
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…
We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is "long-run integration," whereby the…
This paper describes a mechanism for content distribution through opportunistic contacts between subscribers. A subset of subscribers in the network are seeded with the content. The remaining subscribers obtain the information through…
In many real growing networks the mean number of connections per vertex increases with time. The Internet, the Word Wide Web, collaboration networks, and many others display this behavior. Such a growth can be called {\em accelerated}. We…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
We propose a continuum model for the degree distribution of directed networks in free and open-source software. The degree distributions of links in both the in-directed and out-directed dependency networks follow Zipf's law for the…
We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what…
We consider the transmission of a state from the root of a tree towards its leaves, assuming that each transmission occurs through a noisy channel. The states at the leaves are observed, while at deeper nodes we can compute the likelihood…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…
In this paper, a network-based stochastic information propagation model is developed. The information flow is modeled by a probabilistic differential equation system. The numerical solution of these equations leads to the expected number of…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…