Related papers: Degree distribution of shortest path trees and bia…
We consider events over the probability space generated by the degree sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences…
It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…
The multicast capacity of a directed network is closely related to the $s$-$t$ maximum flow, which is equal to the $s$-$t$ minimum cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is…
The load of a node in a network is the total traffic going through it when every node pair sustains a uniform bidirectional traffic between them on shortest paths. We show that nodal load can be expressed in terms of the more elementary…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
We study a discrete-time duplication-deletion random graph model and analyse its asymptotic degree distribution. The random graphs consists of disjoint cliques. In each time step either a new vertex is brought in with probability $0<p<1$…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of the X_i and…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the…
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…