Related papers: How local constraints influence network diameter a…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
This article studies the problem of reconstructing the topology of a network of interacting agents via observations of the state-evolution of the agents. We focus on the large-scale network setting with the additional constraint of…
The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior…
In a recent paper, it has been suggested that the controllability of a diffusively coupled complex network, subject to localized feedback loops at some of its vertices, can be assessed by means of a Master Stability Function approach, where…
We consider local leaders in random uncorrelated networks, i.e. nodes whose degree is higher or equal than the degree of all of their neighbors. An analytical expression is found for the probability of a node of degree $k$ to be a local…
We study the local profiles of trees. We show that, in contrast with the situation for general graphs, the limit set of k-profiles of trees is convex. We initiate a study of the defining inequalities of this convex set. Many challenging…
In this paper we quantify our limited information horizon, by measuring the information necessary to locate specific nodes in a network. To investigate different ways to overcome this horizon, and the interplay between communication and…
Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
Local certification is a mechanism for certifying to the nodes of a network that a certain property holds. In this framework, nodes are assigned labels, called certificates, which are supposed to prove that the property holds. The nodes…
This letter deals with the controllability issue of complex networks. An index is chosen to quantitatively measure the extent of controllability of given network. The effect of this index is analyzed based on empirical studies on various…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
In graph theory and network analysis, node degree is defined as a simple but powerful centrality to measure the local influence of node in a complex network. Preferential attachment based on node degree has been widely adopted for modeling…
Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph…
Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level…
In this article, we prove a local large deviation principle (LLDP) for the empirical locality measure of typed random networks on $n$ nodes conditioned to have a given \emph{ empirical type measure} and \emph{ empirical link measure.} From…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…