Development of algorithms for the conception and the analysis of graphs and complex networks

如有必要，图是由边连接的顶点组成的数学对象。图表对于对某些情况进行建模或促进复杂数据的可视化非常有用。*我的研究项目是与图有关的，即具有期望特征的搜索图、特殊图的研究以及用图来表示复杂信息。*1.寻找极值图*自博士毕业以来，我一直致力于寻找极值图，即具有特殊性质的图。除了可以识别图形的数学性质或找到数学化学中的结果(分子可以用图形表示)外，这种方法最近还允许我的一个学生在他的博士学位期间找到一族与强大的电信网络相对应的图形。我们计划继续朝着这个方向发展，并将优化用于电信网络的设计。在这一领域仍然有相关的应用，但我现在正在考虑将我的研究范围扩大到其他一些相关的问题。*2.对复杂网络的研究*复杂网络，如社会网络，通常是大尺寸的图。复杂网络分析主要基于两个方面：重要顶点的识别和社区的检测。重要顶点的识别是基于中心性的，并允许识别具有关键作用的个人。一个应用可能是病毒式营销问题，其目标是识别有影响力的个人。网络中的社区检测是集群的一个应用，这是我工作多年的一个领域。*3.复杂信息的表示*最后一点，复杂信息的表示，是我在最近一篇关于写作过程表示的工作中进入的一个领域。这一过程包括时间成分和空间成分。一些程序允许记录一个人在用文字处理器或手写图形平板电脑写作时的活动。这些记录产生了大量的数据，人类很难对其进行分析。我们发现，这样的数据可以用图表来建模。这是一种新的表征技术，被语言学家、心理学家和教育学家视为更好地理解这一现象的进步。有理由相信，这样的表象可以扩展到其他涉及空间和时间的过程，并可能在工业工程中应用。

A graph is a mathematical object consisting of vertices connected by edges if necessary. Graphs are useful for modeling some situations or to facilitate the visualization of complex data. ******My research project is related to the graphs, namely the search graph having desired characteristics, the study of particular graphs and the representation of complex information using graphs. ******1. Searching for extreme graphs ******Since my Ph.D, I work on finding extreme graphs, graphs that have special properties. Besides allowing to identify mathematical properties of graphs or finding results in mathematical chemistry (molecules may be represented by graphs), this approach recently allowed one of my students during his Ph.D., to find a family of graphs that correspond to a robust telecommunication networks. We plan to continue in this direction and use optimization for the design of telecommunications networks. There are still relevant applications in that field, however I am now considering extending my research area to some other, related problems. ******2. The study of complex networks ******Complex networks, such as social networks are typically graphs of large size. The complex network analysis is primarily based on two aspects: the identification of important vertices and communities detection. Identification of important vertices is based upon the centrality and allows the identification of individuals who have a key role. An application may be the viral marketing problem where the goal is to identify influent individuals. Communities detection in a network is an application of clustering, an area where I work for years. ******3. The representation of complex information ******The last point, the representation of complex information, is an area in which I entered during a recent work on the representation of the writing process. This process includes a temporal component and a spatial one. Some programs allow the recording of the activity of a person while she writes with a word processor or by hand with a graphical tablet. The records yield a large amount of data that is difficult to analyse by a human. We found that such data may be modelled by a graph. This is a new representation technique that is perceived by linguists, psychologists and educationalists as an advance toward a better understanding of the phenomenon. There are reasons to believe that such a representation could be extended to other processes involving space and time, with possible applications in industrial engineering.