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The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…

Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…

This paper investigates two mechanisms of financial contagion that are, firstly, the correlated exposure of banks to the same source of risk, and secondly the direct exposure of banks in the interbank market. It will consider a random…

Banking fraud causes billion-dollar losses for banks worldwide. In fraud detection, graphs help understand complex transaction patterns and discovering new fraud schemes. This work explores graph patterns in a real-world transaction dataset…

Modelling long-range dependencies is critical for scene understanding tasks in computer vision. Although CNNs have excelled in many vision tasks, they are still limited in capturing long-range structured relationships as they typically…

Feature correspondence selection is pivotal to many feature-matching based tasks in computer vision. Searching for spatially k-nearest neighbors is a common strategy for extracting local information in many previous works. However, there is…

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…

A good computer network is hard to disrupt. It is desired that the computer communication network remains connected even when some of the links or nodes fail. Since the communication links are expensive, one wants to achieve these goals…

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…

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have…

Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…

We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…

We study network robustness under correlated failures modeled by colors, where each color represents a class of edges or vertices that may fail simultaneously. An edge-colored graph is said to be edge-color-avoiding $k$-edge-connected if it…

We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of real-world networks. By extending classical edge connectivity…

This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…

In this paper we offer a novel type of network model which can capture the precise structure of a financial market based, for example, on empirical findings. With the attached stochastic framework it is further possible to study how an…

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…

K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction. However, k-cores can be quite unstable to…

Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…

In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely…