Related papers: Path homology and temporal networks
Temporal information is increasingly available as part of large network data sets. This information reveals sequences of link activations between network entities, which can expose underlying processes in the data. Examples include the…
Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time. Just as network topology can teach us about the system in question, so can its…
We provide an efficient algorithm for determining how a road network has evolved over time, given two snapshot instances from different dates. To allow for such determinations across different databases and even against hand drawn maps, we…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…
Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as networks of telecommunication, neural signal processing, biochemical reactions and human…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex…
Historically studies of behaviour on networks have focused on the behaviour of individuals (node-based) or on the aggregate behaviour of the entire network. We propose a new method to decompose a temporal network into macroscale components…
Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to…
In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…
While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We study a…