Related papers: Electrical Networks with Prescribed Current and Ap…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and…
We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network…
This paper formulates an inverse power flow problem which is to infer a nodal admittance matrix (hence the network structure of a power system) from voltage and current phasors measured at a number of buses. We show that the admittance…
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
The recovery of network structure from experimental data is a basic and fundamental problem. Unfortunately, experimental data often do not directly reveal structure due to inherent limitations such as imprecision in timing or other…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…
Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…