Related papers: Assortativity in networks
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…
The conventional wisdom is that social networks exhibit an assortative mixing pattern, whereas biological and technological networks show a disassortative mixing pattern. However, the recent research on the online social networks modifies…
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node's importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e.…
In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial…
Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original…
This paper introduces a method to generate hierarchically modular networks with prescribed node degree list and proposes a metric to measure network modularity based on the notion of edge distance. The generated networks are used as test…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
A sorting network is a shortest path from $12\dots n$ to $n\dots 21$ in the Cayley graph of the symmetric group $\mathfrak S_n$ spanned by adjacent transpositions. The paper computes the edge local limit of the uniformly random sorting…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
An $r$-augmented tree is a rooted tree plus $r$ edges added from each leaf to ancestors. For $d,g,r\in\mathbb{N}$, we construct a bipartite $r$-augmented complete $d$-ary tree having girth at least $g$. The height of such trees must grow…
In this paper we explore the concept of hierarchy as a quantifiable descriptor of ordered structures, departing from the definition of three conditions to be satisfied for a hierarchical structure: {\em order}, {\em predictability} and {\em…
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
Traditionally, the evolution of cooperation has been studied on single, isolated networks. Yet a player, especially in human societies, will typically be a member of many different networks, and those networks will play a different role in…
The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…
We numerically investigate the robustness of networks with degree-degree correlations between nodes separated by distance $l=2$ in terms of shortest path length. The degree-degree correlation between the $l$-th nearest neighbors can be…
Traceroute measurements are one of our main instruments to shed light onto the structure and properties of today's complex networks such as the Internet. This paper studies the feasibility and infeasibility of inferring the network topology…