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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…

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…

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…

The identification and counting of small graph patterns, called network motifs, is a fundamental primitive in the analysis of networks, with application in various domains, from social networks to neuroscience. Several techniques have been…

One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are…

Network motif provides a way to uncover the basic building blocks of most complex networks. This task usually demands high computer processing, specially for motif with 5 or more vertices. This paper presents an extended methodology with…

Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer…

Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from…

Multiplex networks are a powerful framework for representing systems with multiple types of interactions among a common set of entities. Understanding their structure requires statistical tools capturing higher-order cross-layer…

Studying the topology of so-called 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 networks are…

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…

Motifs are the fundamental components of complex systems. The topological structure of networks representing complex systems and the frequency and distribution of motifs in these networks are intertwined. The complexities associated with…

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…

Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…

Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of…

Transcription networks, and other directed networks can be characterized by some topological observables such as for example subgraph occurrence (network motifs). In order to perform such kind of analysis, it is necessary to be able to…

The randomized technique of color coding is behind state-of-the-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we…

Characterizing motif (i.e., locally connected subgraph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph…

Network motif algorithms have been a topic of research mainly after the 2002-seminal paper from Milo \emph{et al}, that provided motifs as a way to uncover the basic building blocks of most networks. In Bioinformatics, motifs have been…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…