Generating constrained random graphs using multiple edge switches

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily possible to access all graphs obeying some given con- straints through a classical switching procedure calling on pairs of edges. We therefore propose to get round this issue by generalizing this classical approach through the use of higher-order edge switches. This method, which we denote by "k-edge switching", makes it possible to progres- sively improve the covered portion of a set of constrained graphs, thereby providing an increasing, asymptotically certain confidence on the statistical representativeness of the obtained sample.Comment: 15 page

Upper bounds for number of removed edges in the Erased Configuration Model

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected to half-edges of other nodes at random, and then self-loops are removed and multiple edges are concatenated to make the graph simple. Although asymptotic results for many properties of this model, such as the limiting degree distribution, are known, the exact speed of convergence in terms of the graph sizes remains an open question. We provide a first answer by analyzing the size dependence of the average number of removed edges in the erased configuration model. By combining known upper bounds with a Tauberian Theorem we obtain upper bounds for the number of removed edges, in terms of the size of the graph. Remarkably, when the degree distribution follows a power-law, we observe three scaling regimes, depending on the power law exponent. Our results provide a strong theoretical basis for evaluating finite-size effects in networks

Firm-Network Characteristics and Economic Robustness to Natural Disasters

This article proposes a theoretical framework to investigate economic robustness to exogenous shocks such as natural disasters. It is based on a dynamic model that represents a regional economy as a network of production units through the disaggregation of sectorscale Input-Output tables. Results suggest that disaster-related output losses depend on direct losses heterogeneity and on the economic network structure. Two aggregate indexes, concentration and clustering, appear as important drivers of economic robustness, offering opportunities for robustness-enhancing strategies. Modern industrial organization seems to reduce short-term robustness in a trade-off against higher efficiency in normal times.Natural disasters, Economic impacts, Economic Network.

Planar Graph Generation with Application to Water Distribution Networks

The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, in some applications there is a deficiency in real-world data-sets for research purposes due to such reasons as the data sensitivity and high costs for data retrieval. Research related to water distribution networks often relies on synthetic data because the real-world is data is not publicly available due to the sensitivity towards theft and misuse. An important characteristic of water distribution systems is that they can be embedded in a plane, therefore to simulate these system we need realistic networks which are also planar. Currently available synthetic network generators can generate networks that exhibit realism but the planarity is not guaranteed. On the other hand, existing water network generators do not guarantee similarity with the input network and do not scale. In this thesis, we present a flexible method to generate realistic water distribution networks with optimized network parameters such as pipe and tank diameters, tank minimum and maximum levels, and pump sizes. Our model consists of three stages. First, we generate a realistic planar graph from a known water network using the multi-scale randomized edit- ing. Next, we add physical water network characteristics such as pumps, pipes, tanks, and reservoirs to the obtained topology to generate a realistic synthetic water distribution system that can be used for simulation. Finally, we optimize the operational parameters using EPANet simulation tool and multi-objective optimization solver to generate a network with maximum resilience and minimum cost

Modélisation multiniveau de la morphogenèse de familles de citations

Dans cet article, nous étudions les dynamiques de prolifération et de diversification des « citations » dans la blogosphère. Dans la continuité des travaux séminaux de Leskovec et Simmons sur les dynamiques « culturelles » dans les médias sociaux, nous analysons en profondeur les transformations que les citations subissent au cours de leur diffusion en ligne. Nous ne visons pas dans notre approche à modéliser la dynamique temporelle du processus de diffusion mais plutôt de décrire finement la nature des changements qui affectent les expressions placées entre guillemets. Quelles sont les grands types de transformations observées et quelles propriétés des citations les rendent plus ou moins sensibles à ces mutations ? En poursuivant la métaphore biologique, nous essayons de comprendre comment des mutations à différentes échelles génèrent des « espèces » de citations (familles).In this paper we study the dynamics of growth and diversification of quotations in the blogosphere. In line with the seminal work of Leskovec and Simmons on cultural dynamic in social media, we analyze in depth the changes that quotations undergo during their dispersal. In our approach we do not aim to model the temporal dynamics of the diffusion process but rather to accurately describe the nature of the changes that affect quoted texts. What are the major types of changes observed and what properties of the quotations make them more or less prone to these changes ? Following a biological metaphor, we try to understand which way these changes at different scales

Co-presence Analysis and Economic Patterns: Mediterranean Imports in the Celtic World

International audienceThis article presents one of the first steps of a project that aims at exploring the diffusion patterns of Mediterranean imported goods in Late Iron Age Europe (250–25 BC) and the organization of the commercial interactions of these goods. It brings together two archeologists and a mathematician in the study of a large inventory of 57,735 Italian and Greek imports discovered from England to Serbia. This large amount of new and unpublished data is analyzed through the joint use of network analysis tools and formal statistical methods. The analysis focuses on detecting patterns in the association of imported artifacts that are often found on the same sites. The objectives are to highlight groups of imports that may have circulated together and to emphasize regional selections by local populations. At this stage of the study, two main systems of imports have been highlighted used, respectively, in West and Central Europe. Interesting leads that will need further investigation include the imports status and the role they played in Celtic societies, as acculturated objects or more as objects for acculturation