This specialization (within PhD programs in Economics, Political Science, Environmental Science, and Mathematics) awards a non-degree certificate in network science, offered by the Center for Network Science at CEU (CEU CNS). Students will enroll and receive their PhD degrees in either the Department of Economics, Political Science, Environmental Science, or Mathematics. CEU CNS provides an organizational platform for research in network science, with a special focus on applications to practical social problems. The particular strength of the Center is in its diverse interdisciplinary faculty, and the intellectual leadership of Albert-László Barabási, a part-time faculty member of the Center.
Why network science?
Network science, as a maturing field, offers a unique perspective to tackle complex problems, impenetrable to linear-proportional thinking. Networks became part of our everyday experience as we routinely use online social network services, we hear reports on the operations of terrorist networks, and we speculate on the six degrees of separation to celebrities and presidents. Less manifestly, we rely on vast and complex infrastructural networks of electric power distribution, internet data routing, or financial transfers. We only ponder the complexity of these systems when we are faced with avalanche-like dynamics in their collapse, as major blackouts, system stoppages, or financial meltdowns. The science of networks is emerging as a scientific discipline that examines exactly these kinds of interconnections. It aims at explaining complex phenomena at larger scales emerging from simple principles of making network links between nodes.
It seems that networks are everywhere, but network science uses this concept with a careful definition. What is a network in a network science sense? The mere possibility of indentifying nodes and drawing lines between them is different from identifying a network mechanism that explains complex outcomes from simple building blocks. At a railway station for example one could identify travelers as nodes, and draw ties between any two of them if they are headed to the same destination, or if they purchased their ticket from the same teller. These ties however would hardly figure as part of a theoretically sound explanation for individual behavior, or for the emergent functioning of the transit system. If you however drew a network where destinations are nodes, and the number of travelers moving between them is the tie, you can start to identify mechanisms of systemic breakdown in case of a major accident.
While nodes and ties are the fundamental building blocks to any network science approach, the power of network science lies in focusing on triads and beyond: the broader topographical context. Recognizing that connections matter is only the first step: recognizing that ties around dyads matter begins to unleash the power of network science. A tie to a political party might matter for a firm to have access to resources and timely information on policies. Thus far this is a question of connections – is a firm connected to a party? But one can also ask: once a firm is connected to a political party, how are its ties to other firms affected? This becomes a network question: a tie formed at one part of the network system influences the probability of ties elsewhere, and might help explain the emergence of a politically polarized economy.
How to apply?
Applications are handled via the admissions systems of either the 1). Department of Economics, or 2.) the Doctoral School of Political Science, Public Policy and International Relations, 3.) the Department of Environmental Sciences and Policy, 4.) the Department of Mathematics and Its Applications:
For a PhD in Economics with Certificate in Network Science click here
For a PhD in Political Science with Certificate in Network Science click here
For a PhD in Environmental Science with Certificate in Network Science click here
For a PhD in Mathematics with Certificate in Network Science click here
Requirements
In addition to the disciplinary program requirements at either department, PhD students working towards the network science certificate would be required to take one mandatory course on the fundamental ideas in network science, and a total of 4 credits worth of elective courses. In addition, students in these tracks should collaborate with at least one faculty from the Center from Network Science as their first or second reader to conceptualize a dissertation project that engages with debates in network science, uses methods from network science, and has a strong empirical component with original network data collection, or data generation via simulations and experiments.
Mandatory course (4 cr):
Fundamental ideas in network science. 4cr
The aim of this course is to survey the core ideas that constitute the network science field today, in a way that highlights the dense weavings of interdisciplinary connections. Network analysis is applied to a wide diversity of research problems. The course clarifies the key concepts that establish the coherence of this diverse field. Core concepts will be clarified, such as basic elements of graph theory, empirical network characteristics, complexity, scale free systems, emergence, order and chaos. The course will also map out the disciplinary roots of these ideas, in physics, sociology, biology, computer science, mathematics, and will be heavily emprirical based, bringing examples and ideas from different disciplines.
Elective courses (choice of 4cr total)
Social networks. 2cr
Of the many connected systems that are studied from a network perspective the system of social ties is especially important. This course provides an understanding to the basic processes that shape social networks, and the characteristic features of social network systems vis-à-vis technological or ecological networks. The course surveys decades of scholarship in sociology, anthropology, and political science on the fundamental mechanisms of social networking. The key areas include homophily, small world networks, brokerage and conflict, centrality and power, social communities and exclusion.
Economic networks. 2cr
This course presents network concepts from the two distinct perspectives of economics and network science. It aims to provide a background covering both economics concepts and network theory concepts helping to approach problems where network aspects are instrumental to achieve a better description and understanding of the considered problems. The course presents topics as homophily. affiliation, spatial segregation, balanced networks, matching markets as bipartite graphs, trading networks, diffusion in networks, social structure of a firm, network organization of a firm, and international trade network. In some case, along with the introduction of the concepts, the course also presents algorithms that students can use to perform empirical analyses in some specific systems.
Similarity networks. 2cr
Network theory describes complex systems by focusing on the structure and dynamics of networks of elements whose links are originated by direct relationships among the elements of a set. For example, a network of actors is built by connecting all pairs of actors having played together in at least one movie. In the present course we will present a parallel approach using networks as interpretative tools of complex systems of social and economic nature. This will be achieved by considering the properties and the tools used in similarity based networks. A similarity based network is a network obtained starting from a similarity measure characterizing a set of elements belonging to a complex systems. These elements can be as different as, for example, time series of asset returns traded in a financial market, answers of political candidates to a survey, crimes committed by a criminal suspect, etc . The basic similarity measure used is a correlation measure although other similarity measures are possible. Starting from the similarity measure it is possible to obtain classes of similarity networks that can be investigated by using tools and concepts of networks theory. Similarity based networks turns out to be informative about the considered complex systems providing unsupervised approaches to the filtering of relevant information present in them. The course presents how to obtain, validate and interpret the simplest similarity based networks and discusses their ability in filtering relevant information present in social and economic complex systems. Along with the introduction of the concepts underlying similarity based networks, the course also presents the algorithms that students can actively use to apply the concepts to complex systems of their interest.
Computational methods. 2cr
For a successful network scientists, skills in programming and computational methods are essential. This practical course is aimed at refreshing basic programming skills, and providing basic computational tools so that students can write their own code. The course will deal with programming skills needed for practical-logistical purposes. These include basic functions such as reshaping network data across various formats (eg. full matrix, edgelist, nodelist), sorting, recoding, and excerpting data. The course will provide the basic tools for data analysis as well, such as tabulating and plotting descriptives, calculating indices, and testing basic hypotheses. An essential element of network science is a strong visual language. This course also introduces the fundamental principles of drawing effective graphs, and provides the software tools to achieve results.
Graph visualization. 2cr
An essential element of network science is a strong visual language. An effective graph of a network conveys ideas in a forceful manner. This course introduces the fundamental principles of drawing effective graphs, and provides the software tools to achieve results. The primary concern is the placing of network nodes – the course will discuss various approaches (eg. sring embedding, multidimensional scaling, eigenvectors, circular layouts). Beyond layout, other elements of the visual language of graphs will be dealt with, most importantly ways to represent weighted and multiple relations, drawing hierarchical systems, and representing attribute data. Students will be encouraged to enter international annual graph drawing competitions with their class projects.
Random graphs and network simulations. 2cr
In testing any theoretical arguments about network structure one needs a baseline of comparison. While in conventional statistics the baseline is readily available (in the form of, for example, the chi-squared distribution), in networks the baseline is highly complex. A common approach to establish a baseline network structure is to rely on random graphs. This course introduces conceptions of random graphs from the Erdos-Renyi model to biased random graphs, preferential attachment processes, small world structures, and random rewiring. The course builds on computational skills to write computer code for random graph-based simulations
