Related papers: Revisiting Graph Homophily Measures
Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels…
A prominent threat to causal inference about peer effects over social networks is the presence of homophily bias, that is, social influence between friends and families is entangled with common characteristics or underlying similarities…
As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar) while their…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
Graph Neural Networks (GNNs) have achieved significant success in various learning tasks on graph-structured data. Nevertheless, most GNNs struggle to generalize to heterophilic neighborhoods. Additionally, many GNNs ignore the directional…
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…
Several important complex network measures that helped discovering common patterns across real-world networks ignore edge weights, an important information in real-world networks. We propose a new methodology for generalizing measures of…
Signed graphs are studied since the middle of the last century. Recently, the notion of homomorphism of signed graphs has been introduced since this notion captures a number of well known conjectures which can be reformulated using the…
As implied by the plethora of literature on graph rewiring, the choice of computational graph employed by a neural network can make a significant impact on its downstream performance. Certain effects related to the computational graph, such…
Kemeny's constant quantifies a graph's connectivity by measuring the average time for a random walker to reach any other vertex. We introduce two concepts of the directional derivative of Kemeny's constant with respect to an edge and use…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar…
Recently, neighbor-based contrastive learning has been introduced to effectively exploit neighborhood information for clustering. However, these methods rely on the homophily assumption-that connected nodes share similar class labels and…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…