Related papers: Preferential attachment hypergraph with high modul…
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…
We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent…
We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
We study the preferential attachment model $G_n^h$. A graph $G_n^h$ is generated from a finite initial graph by adding new vertices one at a time. Each new vertex connects to $h\ge 1$ already existing vertices, and these are chosen with…
The preferential attachment (PA) process is a popular theory for explaining network power-law degree distributions. In PA, the probability that a new vertex adds an edge to an existing vertex depends on the connectivity of the target…
Users of social networks display diversified behavior and online habits. For instance, a user's tendency to reply to a post can depend on the user and the person posting. For convenience, we group users into aggregated behavioral patterns,…
Mutualism is a biological interaction mutually beneficial for both species involved, such as the interaction between plants and their pollinators. Real mutualistic communities can be understood as weighted bipartite networks and they…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
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.…
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…
We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…
We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost)…
Reciprocity in social networks helps understand information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study indicates the reciprocity coefficient of a classical directed…
The rapid spread of information and rumors through social media platforms, especially in group settings, motivates the need for more sophisticated models of rumor propagation. Traditional pairwise models do not account for group…
We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
The ability to sample random networks that can accurately represent real social contact networks is essential to the study of viral epidemics. The Barab\'asi-Albert model and its extensions attempt to capture reality by generating networks…