Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Systems and methods for forming an adjacency graph for exchanging network routing data

Abstract: A system for exchanging routing information over a communications network constructs a connectivity graph that indicates connectivity between a first node and a first set of nodes in the network. The system constructs an adjacency graph that indicates a second set of nodes with which the first node will exchange routing data, where the adjacency graph is distinct from the connectivity graph. The system exchanges routing data between the first node and each node of the second set of nodes based on the adjacency graph.

Graph Grammars for distributed systems

Abstract: In the paper we define grammars on a class of labeled, partially ordered hypergraphs, called distributed systems. A distributed system models both the spatial and the temporal aspects of a real system through the relations of adjacency and causality. Terminal symbols represent the (deterministic, certain) past history of the system while nonterminal symbols model the (possibly nondeterministic, potential) future history of the system. The (context free) productions of a grammar represent the possible stand-alone evolutions of system components. From the productions, we obtain a (possibly infinite) number of rewriting rules, which model the synchronized evolution of adjacent system components. The (terminal) distributed systems derived within a given grammar represent the alternative deterministic, concurrent computations of a single nondeterministic system which is thus completely modeled by the grammar.

Accuracy criterion for the mean-field approximation in susceptible-infected-susceptible epidemics on networks.

Abstract: Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovian susceptible-infected-susceptible (SIS) epidemics on any network, based on the spectrum of the adjacency and SIS covariance matrix. We evaluate the MFA criterion for the complete and star graphs analytically, and numerically for connected Erdős-Renyi random graphs for small size N≤14. The accuracy of MFA increases with average degree and with N. Precise simulations (up to network sizes N=100) of the MFA accuracy criterion versus N for the complete graph, star, square lattice, and path graphs lead us to conjecture that the worst MFA accuracy decreases, for large N, proportionally to the inverse of the spectral radius of the adjacency matrix of the graph.

Visualization of large networks with min-cut plots, A-plots and R-MAT

Abstract: What does a ''normal'' computer (or social) network look like? How can we spot ''abnormal'' sub-networks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal money-laundering rings), forecasting, and simulations (''how will a computer virus spread?''). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such patterns and ''laws'', including the ''min-cut plots'' discovered by us. This is the first part of our NetMine package: given any large graph, it provides visual feedback about these patterns; any significant deviations from the expected patterns can thus be immediately flagged by the user as abnormalities in the graph. The second part of NetMine is the A-plots tool for visualizing the adjacency matrix of the graph in innovative new ways, again to find outliers. Third, NetMine contains the R-MAT (Recursive MATrix) graph generator, which can successfully model many of the patterns found in real-world graphs and quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. We present results on multiple, large real graphs, where we show the effectiveness of our approach.

Consistency constraints and 3D building reconstruction

Abstract: Virtual architectural (indoor) scenes are often modeled in 3D for various types of simulation systems. For instance, some authors propose methods dedicated to lighting, heat transfer, acoustic or radio-wave propagation simulations. These methods rely in most cases on a volumetric representation of the environment, with adjacency and incidence relationships. Unfortunately, many buildings data are only given by 2D plans and the 3D needs varies from one application to another. To face these problems, we propose a formal representation of consistency constraints dedicated to building interiors and associated with a topological model. We show that such a representation can be used for: (i) reconstructing 3D models from 2D architectural plans (ii) detecting automatically geometrical, topological and semantical inconsistencies (iii) designing automatic and semi-automatic operations to correct and enrich a 2D plan. All our constraints are homogeneously defined in 2D and 3D, implemented with generalized maps and used in modeling operations. We explain how this model can be successfully used for lighting and radio-wave propagation simulations.