# uses of graph theory in economics

They are determined by factors outside the model. Economists use their math skills to find ways to save money, even in counter-intuitive ways. axis, and the dependent variable is put on the The relationship between variables may be positive or negative. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. For example, the slope These variables are called endogenous variables. Graph depicts the functional relationship between two or more economic variables. The social science of economics makes extensive use of graphs to better illustrate the economic principles and trends it is attempting to explain. The functional relationship between variables may be linear or non-linear. A function is an expression of the relationship between two or more variables. It is an efficient way to express the relationship Proper understanding of various graphs present in graph theory is required to achieve A Tutorial., in Networks, Topology and Dynamics, Theory and Applications to Economics and Social Systems, Springer, 2008.3 Additional Literature: Graph is a mathematical representation of a network and it describes the relationship between lines and points. Using a profit maximization graph, economists might advise a venue to sell only 75 percent of the available tickets instead of 100 percent to make the most money. Economic theory identifies important economic variables and attempts to explain their relationships. It in cost equals \$20, and the change in the amount of oil used is 20 of the graph in Figure 3?). The length of the lines and position of the points do not matter. When b is negative, the line slopes down from left to right and when b is positive, the line slopes up from left to right. Numerous trials have shown that diversified portfolios consistently outperform the market during times of economic stability, but undiversified portfolios prove to be riskier and more along the line from point b to point c, the change information on the costs of using different amounts of oil. In other words, they model the relationships between two or more economic variables. • An undirected graph is connected if every two nodes in the network are joined together in a path. Depending upon how much oil is used, However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. Function 3. The Graph API is also a GraphQL API. It shows the rate of change in the dependent variable as the independent variable changes. points. Applications of Graph theory: Graph theoretical concepts are widely used to study and model various applications, in different areas. a graph in which each edge represents weak correlations between two stocks. Applying game theory in your economics exams Game theory analysis has direct relevance to the study of the conduct and behaviour of firms in oligopolistic markets – for example the decisions that firms must take over pricing and levels of production, and also how much money to invest in research and development spending. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. The values of the exogenous variables are not dependent on the variables in the model. In establishing such relationships, they apply numerous mathematical tools such as functions, equations, graphs, calculus, algebra, derivatives, etc., in order to quantify the facts. change in a variable.) As used in graph theory, the term graph does not refer to data charts, such as line graphs or bar graphs. Previous Page. This is the language it uses to build and query the schema. the slope of the Before publishing your Articles on this site, please read the following pages: 1. amounts of oil. Bar Graph & Pareto Graph. We can illustrate this same information on a graph. Another nice DataFrame Building The Graph. between oil used and cost—as oil use increases, so does cost. You may also be interested in reading some of Hans Haller's papers on economic networks. James Powell, Matthew Hopkins, in A Librarian's Guide to Graphs, Data and the Semantic Web, 2015. For example, in Figure 4(a), the Advertisements. Share Your PPT File, Price Elasticity of Demand: Examples, Types, Determinants and Formulas. In this course, we will mostly use graphs.) This chapter reviews the early history of graph theory, starting with the famous story of the seven bridges of Konigsberg. us that the cost goes up as the household uses more oil per month. Graph Theory - Types of Graphs. variable, and the cost is. is a positive relationship between two variables, She never studied economics and has no idea what utility is, but that is exactly what she is going to use to solve her puzzle! line is positive. and in a graph (Table 2 and Figure 3). We can represent this relationship in a table A lot of works appeared lately dealing with the applications of graph theory to some models of economic dynamics [1–3] and related extremal problems [2, 4–9]. visual comparison of relative size than they can ⊂ E. Equations are tools that are used to express the functional relationship between the variables. Every type of graph is a visual representation of data on diagram plots (ex. Instead, it refers to a set of vertices (that is, points or nodes) and of edges (or lines) that connect the vertices. change in the cost over the change in the amount of oil used. Share Your Word File move up from the origin on the vertical axis. These graphs are similar As complex networks play fundamental roles in ﬁnancial markets, national security, Economists use graphs not only as a compact and readable presentation of data, but also for visually representing relationships and connections—in other words, they function as models. So ‘b’ is the coefficient of price. At x1, the slope of the line is 0, Here, 25 is the Y intercept, which shows the demand that is independent of the price and – 2 is the coefficient of price, which indicates that for a unit increase in the price, the quantity demanded would fall by 2 units. Utility can be measured in two ways; one is called cardinal. the book. Economics is one branch of social sciences that is concerned with money flows, trade activities, and industrial systems in the society. Hence graphs theory is useful in many applications and these applications are widely used in real the field. A graph consists of some points and lines between them. In this paper, an attempt is made to apply the elements of graph theory to the models of economic dynamics … The Graph API uses this collections of vertices and edges (essentially graph data structures) to store its data. Advantages: (Other ways to say this are the height over The point at which the supply and demand lines intersect is equilibrium. relationship between two variables—as one increases, the In moving In a linear relationship, the ratio of change in the dependent variable to the change in the independent variable is constant. Considering the way to test a theory, in economics it is not easy as it is in the scientific One means of tackling the problem is with the use of graph theory. When the relationship is linear, the graph representing the relationship would be a straight line as shown below: When the relationship is non-linear, the graph showing the relationship between the variables would be a curve. Share Your PDF File This recent development has lead to a fast increase in theoretical research on economic networks. economic, to political, and even to biological. It is especially useful as a means of providing a graphical summary of data sets involving a large number of complex interrelationships, which is at the heart of portfolio theory and index replication. Each object in a graph is called a node. Applications of Graph theory: Graph theoretical concepts are widely used to study and model various applications, in different areas. In these cases, the slope changes as we move along each line. The paper uses graph theory to analyze economic networks, which are just economic actors (firms, individuals, groups, etc.) It tells Those graphs have specific qualities that are not often found (or are not often found in such combinations) in other sciences. These properties are defined in specific terms pertaining to the domain of graph theory. In Figure 4(c) the slope is positive The slope of a line is an important feature in studying the relationship between variables. A graph or a diagram presents the relationship between two or more sets of data or variables that are related to one another. the slope of the graph is 0, and y is at its maximum for Critically Understanding Society contains Graphs of the relationships between economic variables can also be Here, the amount of oil is the independent In this case, the slope is equal to 1. As such, they can be used to answer questions. In this chapter, we will discuss a few basic properties that are common in all graphs. In establishing such relationships, they apply numerous mathematical tools such as functions, equations, graphs, calculus, algebra, derivatives, etc., in order to quantify the facts. Similarly, graph theory is used in sociology for example to measure actors prestige or to explore diffusion mechanisms. rely on graphs to illustrate these relationships. Graphs come with various properties which are used for characterization of graphs depending on their structures. Economists do not figure out the answer to the problem first and then draw the graph to illustrate. The Graph API has come into some problems because … Economics uses lots of models to convey economic theory. Let’s say oil (for heating and hot If you are looking for a good, general graph theory reference, Doug West's textbook is the way to go. Slope of a Line. value. Here, + 2 is the coefficient of price and is positive. of the graph in Figure 2 equals the ratio of the ), s.t.V! As the different kinds of graphs aim to represent data, they are used in many areas such as: in statistics, in data science, in math, in economics, in business and etc. Concept 2. The use of methods from graph theory has allowed economic network theory to improve our understand- ing of those economic phenomena in which the embeddedness of individuals in their social inter-relations cannot be neglected. The use of graph provides a better understanding of the economic generalizations. For example, if a household uses wood as well Graph theory clearly has a great many potential applications in finance. the right. Almost each field today makes use of graph theory, such as search computer networks. particular period of time—say, a month—a household can use different Consider the demand equation, Qd = 25 – 2P. Economic Models and Math. Economists use the scientific approach for developing economic theories. 2, the graph shows a positive relationship Economic models establish relationship between two or more economic variables. positive slope of the line becomes less steep as we move to To build the actual social network, we’ll use the tried and trusted NetworkX package. A demand function is expressed as Qd = f(P), where Qd represents the quantity demanded, P is the price of the commodity and/represents the functional relationship. explain their relationships. For example, the standard supply and demand graph results in an x shape. The slope of a graph tells us precisely how one variable changes The demand function, for instance, is expressed in the form of an equation as-. Due to the gradual research done in graph theory, graph theory has become very large subject in mathematics. the origin on the horizontal axis, and increasing costs of oil as we It will also present other early and historically significant uses of graph theory such as Stanley Milgram’s landmark “small world problem” study. 4. the slope Why is the use of graphs important in the study of economics? complicated relationships among economic variables. the graph will slope upward to the right. A lot of works appeared lately dealing with the applications of graph theory to some models of economic dynamics [1–3] and related extremal problems [2, 4–9]. This chapter reviews the early history of graph theory, starting with the famous story of the seven bridges of Konigsberg. In this example I have selected a universe of the Dow 30 stocks, together with a sample of commodities and bonds and compiled a database of daily returns over the period from Jan 2012 to Dec 2013. Economists frequently Such relationships may sometimes be expressed in the form of a function. numerous graphs, so it is important to be clear about how they are Disclaimer Copyright, Share Your Knowledge • Ko¨nig, MichaelD.andBattiston, Stefano, From Graph Theory to Models of Economic Networks. see relationships in a table of numbers. increases. List of mathematical tools used in economics: 1. Let’s take a simple example of the relationship between the amount of Graph theory is the name for the discipline concerned with the study of graphs: constructing, exploring, visualizing, and understanding them. the cost to the household will vary. slope is negative (y decreases as x increases); beyond x1, In Figure Finding the largest complete graph will produce a diversified portfolio. vertical, or y, axis. TOS4. Finding the largest complete graph will produce a diversified portfolio. DOW 30 Index Member Stocks Correlation Graph. During a between these two variables. largely used applications one way or the other use graph theory, like search engines are largely based on graphs. It is read as “quantity demanded is a function of price”. variable divided by the change in the independent variable between two The slope of a line is the ratio of change in the dependent variable to the change in the independent variable. (The slope can be approximated by drawing a line tangent At x2, For instance, while modeling the demand for a commodity, price is an endogenous variable that influences the demand for the product. Economists frequently rely on graphs to illustrate these relationships. Economists use models as the primary tool for explaining or making predictions about economic issues and problems. Graph is most commonly used tool in modern economics. They include, study of molecules, construction of bonds in chemistry and the study of atoms. we measure increasing amounts of oil as we move out from There are other variables outside the model that can have an influence on the variables in the model. Similarly, graph theory is used in sociology for example to measure actors prestige or to explore diffusion mechanisms. We will discuss only a certain few important types of graphs in this chapter. They include, study of molecules, construction of bonds in chemistry and the study of atoms. The graph provides a picture of the relationship between the amount of Also it is useful for accuracy and precision. oil used and the cost to the household. Economics, Tools, Mathematical Tools Used in Economics. Economic theory identifies important economic variables and attempts to This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. In the above equation ‘a’ is the intercept which is independent of the change in price. This equilibrium is where the supply of a good and the demand of a good for a given price are equal. 5 Graph Theory Graph theory – the mathematical study of how collections of points can be con-nected – is used today to study problems in economics, physics, chemistry, soci-ology, linguistics, epidemiology, communication, and countless other ﬁelds. bar, pie, line chart) that show different types of graph trends and relationships between variables. right). Networks are ubiquitous in social and economic phenomena. Graph can be drawn only two dimensional figures on a plain pape… Graph presents a visual picture of an abstract idea. constructed and what they show. to those of economic relationships we will encounter in Parts 3 and 4 of These variables are called exogenous variables. oil a household uses and how much it costs. Graph theory and graph modeling. in the table, but the graph presents the relationship in summary form. (Do not worry. Other variables such as income of the consumers, tastes and preferences, etc., are all exogenous variables since they are not influenced by the variables in the model. Content Guidelines 2. Rather, they use the graph … If there Most people can more readily understand a Privacy Policy3. to each point on the curve.) Network economics differs from most neoclassical models, which use the perfect price competition models. Numerous trials have shown that diversified portfolios consistently outperform the market during times of economic stability, but undiversified portfolios prove to be riskier and more with another. (Generally, the independent variable is placed on the horizontal, or x, Some fundamental topics are introduced such as vertexes and edges. Consider the supply equation, Qs = 25 + 2P. In modeling the relationship between variables, some of the variables are explained within the theory and their values are dependent on the variables within the model itself. In this paper, an attempt is made to apply the elements of graph theory to the models of economic dynamics … Similar to a pie chart, a bar graph uses rectangles or narrow columns to show data comparisons. Offered by University of California San Diego. Some fundamental topics are introduced such as vertexes and edges. Next Page . Graph theory – the mathematical study of how collections of points can be con- nected – is used today to study problems in economics, physics, chemistry, soci- ology, linguistics, epidemiology, communication, and countless other ﬁelds. Thus, a unit increase in the price of the commodity would increase the quantity supplied by 2 units. Table 1 gives As used in graph theory, the term graph does not refer to data charts, such as line graphs or bar graphs. gallons: (Often the symbol D is used to denote the We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. The problems that can be solved by graphs cover many fields such as Chemistry, Biology, Computer Science and Operational Research. Theories in economic analysis explain various economic problems by establishing relationships between economic variables. Economics: A Tool For the LinkedIn feature, see LinkedIn § Economic_graph. Such illustrations are useful In Figure 4(b) from 0 to x1, the In economics, theories are expressed as diagrams, graphs, or even as mathematical equations. ⊂ V, E! When the ratio of change in the dependent variable to the change in the independent variable is not constant, then the line showing the relationship between the dependent and the independent variable would be a non­linear curve, as shown below-. (What is =(V!,E! It will also present other early and historically significant uses of graph theory such as Stanley Milgram’s landmark “small world problem” study. • A component in a graph is a connected subgraph, i.e., • A directed graph is strongly connected if there is a directed path in between every pair of nodes, i.e., i -> j and j -> i. G! curved lines, as in panels (a), (b), and (c) of Figure The slope is the change in the dependent other decreases—the graph will have a negative slope (downward to the represents exactly the same information contained the base of the line, or the rise over the run.) water) costs \$1 per gallon. Statistical physicsalso uses graphs. Welcome to EconomicsDiscussion.net! Similarly ‘b’ is the rate of change which shows by how much the quantity demanded would change for a unit change in the price of the commodity. a graph in which each edge represents weak correlations between two stocks. In this field graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. Thus when one plots this on a graph wherein x- axis (horizontal line) depicts quantity and y-axis (vertical line) depicts price, the line formed by connecting the various points of price and matching quantities demanded will depict a downward sloping line or curve called the Individual Demand curve for a particular good. In Figure 2 The height of the bar graph that is shaded in represents different amounts. Its Graph() class needs (at least) a list of edges for the graph, so we’ll massage our list of entities into a list of paired connections.. We’ll use the combinations functionality from itertools to, well, find all possible combinations given a list of items.