Related papers: Minimal Construction of Graphs with Maximum Robust…
A directed acyclic graph $G=(V,E)$ is said to be $(e,d)$-depth robust if for every subset $S \subseteq V$ of $|S| \leq e$ nodes the graph $G-S$ still contains a directed path of length $d$. If the graph is $(e,d)$-depth-robust for any $e,d$…
The structure of many financial networks is protected by privacy and has to be inferred from aggregate observables. Here we consider one of the most successful network reconstruction methods, producing random graphs with desired link…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes…
The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…
In this paper, we introduce a new model to study network reliability with node failures. This model, strongly connected node reliability, is the directed variant of node reliability and measures the probability that the operational vertices…
We consider network models where information items flow %are sent from a source to a sink node. We start with a model where routing is constrained by energy available on nodes in finite supply (like in Smartdust) and efficiency is related…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
In the real world, networks often contain multiple relationships among nodes, manifested as the heterogeneity of the edges in the networks. We convert the heterogeneous networks into multiple views by using each view to describe a specific…
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space $\mathbb{R}^d$ or on a sphere and which in addition satisfy certain edge length constraints. One of the major open problems in this field…
Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given…