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We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…
Graphs are often used to model relationships between entities. The identification and visualization of clusters in graphs enable insight discovery in many application areas, such as life sciences and social sciences. Force-directed graph…
Bipartite graphs are widely used to model relationships between two types of entities. Community search retrieves densely connected subgraphs containing a query vertex, which has been extensively studied on unipartite graphs. However,…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
The "abstract search algorithm" is a well known quantum method to find a marked vertex in a graph. It has been applied with success to searching algorithms for the hypercube and the two-dimensional grid. In this work we provide an example…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…
Consensus strategies find a variety of applications in distributed coordination and decision making in multi-agent systems. In particular, average consensus plays a key role in a number of applications and is closely associated with two…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…