Related papers: Fast and Scalable Complex Network Descriptor Using…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Personalized PageRank (PPR) is a traditional measure for node proximity on large graphs. For a pair of nodes $s$ and $t$, the PPR value $\pi_s(t)$ equals the probability that an $\alpha$-discounted random walk from $s$ terminates at $t$ and…
In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
This paper develops a generalization of the PageRank model of page centralities in the global webgraph of hyperlinks. The webgraph of adjacencies is generalized to a valued directed graph, and the scalar dampening coefficient for walks…
We investigate the problem of enforcing a desired centrality measure in complex networks, while still keeping the original pattern of the network. Specifically, by representing the network as a graph with suitable nodes and weighted edges,…
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.…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a…
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…
A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…
Node influence metrics have been applied to many applications, including ranking web pages on internet, or locations on spatial networks. PageRank is a popular and effective algorithm for estimating node influence. However, conventional…
We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…