Related papers: Fractality of Massive Graphs: Scalable Analysis wi…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
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…
Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…
Network dismantling is to identify a minimal set of nodes whose removal breaks the network into small components of subextensive size. Because finding the optimal set of nodes is an NP-hard problem, several heuristic algorithms have been…
K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…
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…
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from…
This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from noise, we…
The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…
Song, Havlin and Makse (2005) have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number $N_V$ of boxes of size $\ell$ needed…
Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…
We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks…
Surface cracks are a very common indicator of potential structural faults. Their early detection and monitoring is an important factor in structural health monitoring. Left untreated, they can grow in size over time and require expensive…
Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…