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

图是由顶点组成的数学对象，必要时由边连接。图形对于某些情况的建模或促进复杂数据的可视化非常有用。******我的研究项目与图有关，即具有期望特征的搜索图，特定图的研究以及用图表示复杂信息。* * * * * * 1。搜索极值图******自从我获得博士学位以来，我一直致力于寻找具有特殊属性的极值图。除了允许识别图的数学性质或发现数学化学的结果（分子可以用图表示），这种方法最近允许我的一个学生在他的博士学位期间，找到一个与健壮的电信网络相对应的图族。我们计划继续朝这个方向发展，并在电信网络的设计中使用优化。在这个领域仍然有相关的应用，但是我现在正在考虑将我的研究领域扩展到其他一些相关的问题。* * * * * * 2。复杂网络的研究******复杂网络，如社交网络，通常是大尺寸的图。复杂网络分析主要基于两个方面：重要点的识别和群落的检测。重要顶点的识别基于中心性，并允许识别具有关键作用的个体。应用程序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聚类的一种应用，这是我研究多年的领域。* * * * * * 3。复杂信息的表示******最后一点，复杂信息的表示，是我在最近一项关于写作过程表示的工作中进入的一个领域。这个过程包括时间部分和空间部分。有些程序允许记录一个人在用文字处理机或手写图形平板电脑写作时的活动。这些记录产生了人类难以分析的大量数据。我们发现这样的数据可以用图表来表示。语言学家、心理学家和教育学家认为，这是一种新的表征技术，有助于更好地理解这一现象。有理由相信，这种表示可以扩展到涉及空间和时间的其他过程，并可能应用于工业工程。

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.