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Temporal bipartite graphs are widely used to denote time-evolving relationships between two disjoint sets of nodes, such as customer-product interactions in E-commerce and user-group memberships in social networks. Temporal butterflies,…

Social and Information Networks · Computer Science 2023-10-19 Jiaxi Pu , Yanhao Wang , Yuchen Li , Xuan Zhou

Understanding the dynamics of financial transactions among people is critical for various applications such as fraud detection. One important aspect of financial transaction networks is temporality. The order and repetition of transactions…

Social and Information Networks · Computer Science 2025-07-14 Penghang Liu , Bahadir Altun , Rupam Acharyya , Robert E. Tillman , Shunya Kimura , Naoki Masuda , Ahmet Erdem Sarıyüce

Bipartite graphs characterize relationships between two different sets of entities, like actor-movie, user-item, and author-paper. The butterfly, a 4-vertices 4-edges (2,2)-biclique, is the simplest cohesive motif in a bipartite graph and…

Data Structures and Algorithms · Computer Science 2026-04-21 Xinwei Cai , Xiangyu Ke , Kai Wang , Lu Chen , Tianming Zhang , Qing Liu , Yunjun Gao

We introduce a new method for finding network motifs: interesting or informative subgraph patterns in a network. Subgraphs are motifs when their frequency in the data is high compared to the expected frequency under a null model. To compute…

Machine Learning · Computer Science 2021-04-19 Peter Bloem , Steven de Rooij

Many real-world phenomena are best represented as interaction networks with dynamic structures (e.g., transaction networks, social networks, traffic networks). Interaction networks capture flow of data which is transferred between their…

Social and Information Networks · Computer Science 2018-10-22 Chrysanthi Kosyfaki , Nikos Mamoulis , Evaggelia Pitoura , Panayiotis Tsaparas

Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…

Physics and Society · Physics 2017-11-08 Luis E C Rocha , Naoki Masuda , Petter Holme

Studying the topology of so-called {\em real networks}, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that…

Applications · Statistics 2010-11-23 Etienne Birmele

Graph motif, defined as the microstructure that appears repeatedly in a large graph, reveals important topological characteristics of the large graph and has gained increasing attention in power system analysis regarding reliability,…

Systems and Control · Electrical Eng. & Systems 2024-12-10 Yiyan Li , Zhenghao Zhou , Jian Ping , Xiaoyuan Xu , Zheng Yan , Jianzhong Wu

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…

Data Analysis, Statistics and Probability · Physics 2011-11-15 Lauri Kovanen , Márton Karsai , Kimmo Kaski , János Kertész , Jari Saramäki

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series.…

Data Structures and Algorithms · Computer Science 2026-03-20 Matteo Ceccarello , Francesco Pio Monaco , Francesco Silvestri

Algorithms for mining very large graphs, such as those representing online social networks, to discover the relative frequency of small subgraphs within them are of high interest to sociologists, computer scientists and marketeers alike.…

Social and Information Networks · Computer Science 2017-06-16 Guyue Han , Harish Sethu

With the growing amount of available temporal real-world network data, an important question is how to efficiently study these data. One can simply model a temporal network as either a single aggregate static network, or as a series of…

Social and Information Networks · Computer Science 2014-12-15 Yuriy Hulovatyy , Huili Chen , Tijana Milenkovic

Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…

Data Structures and Algorithms · Computer Science 2025-03-14 Talya Eden , Reut Levi , Dana Ron , Ronitt Rubinfeld

Networks of timestamped interactions arise across social, financial, and biological domains, where forecasting future events requires modeling both evolving topology and temporal ordering. Temporal link prediction methods typically frame…

Machine Learning · Computer Science 2026-03-09 İbrahim Bahadır Altun , Ahmet Erdem Sarıyüce

A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and…

Social and Information Networks · Computer Science 2020-04-02 Taha Sevim , Muhammet Selçuk Güvel , Lale Özkahya

Financial fraud detection is essential to safeguard billions of dollars, yet the intertwined entities and fast-changing transaction behaviors in modern financial systems routinely defeat conventional machine learning models. Recent…

Machine Learning · Computer Science 2025-08-29 Zeyue Zhang , Lin Song , Erkang Bao , Xiaoling Lv , Xinyue Wang

The discovery of time series motifs has emerged as one of the most useful primitives in time series data mining. Researchers have shown its utility for exploratory data mining, summarization, visualization, segmentation, classification,…

Machine Learning · Computer Science 2018-02-16 Yan Zhu , Abdullah Mueen , Eamonn Keogh

Temporal networks are essential for modeling and understanding systems whose behavior varies in time, from social interactions to biological systems. Often, however, real-world data are prohibitively expensive to collect in a large scale or…

Social and Information Networks · Computer Science 2023-08-23 Antonio Longa , Giulia Cencetti , Sune Lehmann , Andrea Passerini , Bruno Lepri

Counting the frequencies of 3-, 4-, and 5-node undirected motifs (also know as graphlets) is widely used for understanding complex networks such as social and biology networks. However, it is a great challenge to compute these metrics for a…

Social and Information Networks · Computer Science 2015-12-18 Pinghui Wang , Jing Tao , Junzhou Zhao , Xiaohong Guan

Diffusion models simulate the propagation of influence in networks. The design and evaluation of diffusion models has been subjective and empirical. When being applied to a network represented by a graph, the diffusion model generates a…

Social and Information Networks · Computer Science 2020-12-15 Fangqi Li