Related papers: Synchronization Properties of Network Motifs
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We introduce a method to find network motifs in knowledge graphs. Network motifs are useful patterns or meaningful subunits of the graph that recur frequently. We extend the common definition of a network motif to coincide with a basic…
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…
Structural balance theory predicts that triads in networks gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for…
The lifestyles of urban dwellers could reveal important insights regarding the dynamics and complexity of cities. Despite growing research on analysis of lifestyle patterns in cities, little is known about the characteristics of people's…
Motifs, which have been established as building blocks for network structure, move beyond pair-wise connections to capture longer-range correlations in connections and activity. In spite of this, there are few generative graph models that…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
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…
A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed…
Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks.…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the…
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…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…