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Causal networks are useful in a wide variety of applications, from medical diagnosis to root-cause analysis in manufacturing. In practice, however, causal networks are often incomplete with missing causal relations. This paper presents a…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…
Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…
For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory…
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
Force-directed (FD) algorithms can be used to explore relationships in social networks, visualize money markets, and analyze transaction networks. However, FD algorithms are mainly designed for visualizing static graphs in which the…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…