Graphic Organizers Final

GRAPHICORGANIZERS

TREE MAPTree maps are ideal for displaying large amounts of hierarchically structured (tree-structured) data. The space in the visualization is split up into rectangles that are sized and ordered by a quantitative variable.

The levels in the hierarchy of the tree map are visualized as rectangles containing other rectangles. Each set of rectangles on the same level in the hierarchy represents a column or an expression in a data table. Each individual rectangle on a level in the hierarchy represents a category in a column. For example, a rectangle representing a continent may contain several rectangles representing countries in that continent. Each rectangle representing a country may in turn contain rectangles representing cities in these countries. You can create a tree map hierarchy directly in the visualization, or use an already defined hierarchy. To learn more, see the sectionTo Create a Tree map Hierarchy.

A number of different algorithms can be used to determine how the rectangles in a tree map should be sized and ordered. The tree map in Spot fire uses a squarified algorithm.

The rectangles in the tree map range in size from the top left corner of the visualization to the bottom right corner, with the largest rectangle positioned in the top left corner and the smallest rectangle in the bottom right corner. For hierarchies, that is, when the rectangles are nested, the same ordering of the rectangles is repeated for each rectangle in the tree map. This means that the size, and thereby also position, of a rectangle that contains other rectangles is decided by the sum of the areas of the contained rectangles.

TREE MAP

FISHBOWL

Four to five chairs are arranged in an inner circle. This is the fishbowl. The remaining chairs are arranged in concentric circles outside the fishbowl. A few participants are selected to fill the fishbowl, while the rest of the group sit on the chairs outside the fishbowl. In anopen fishbowl, one chair is left empty. In aclosed fishbowl, all chairs are filled. The moderator introduces the topic and the participants start discussing the topic. The audience outside the fishbowl listens in on the discussion.In an open fishbowl, any member of the audience can, at any time, occupy the empty chair and join the fishbowl. When this happens, an existing member of the fishbowl must voluntarily leave the fishbowl and free a chair. The discussion continues with participants frequently entering and leaving the fishbowl. Depending on how large your audience is you can have many audience members spend some time in the fishbowl and take part in the discussion. When time runs out, the fishbowl is closed and the moderator summarizes the discussion.In a closed fishbowl, the initial participants speak for some time. When time runs out, they leave the fishbowl and a new group from the audience enters the fishbowl. This continues until many audience members have spent some time in the fishbowl. Once the final group has concluded, the moderator closes the fishbowl and summarizes the discussion.AdvantagesAn advantage of a fishbowl conversation is that it is suitable for large groups. Another advantage is that they lessen distinctions between the speakers and the audience. These two reasons have made fishbowls popular in participatory group meetings and conferences such as Open Space Technology andUnconferences.VariationThe group can be split into two smaller and distinct subgroups (such as men and women, or older and younger participants), who convene separately and come up with three to four questions for the other group, which are written on cards. The participants reconvene and exchange cards, and form two circles, one subgroup inside the other, both of them facing inwards. The inside group read a question and discuss it, while those in the outside circle listen but do not speak. Each question is discussed in this way, making sure everyone in the inner circle has a chance to speak. The circles are then reversed. The questions that the groups generate can be on the same subject or not, at the discretion of the organizer. This version is a good party game for groups of thirty to sixty people.

FISHBOWL

T-ChartA T-Chart is used for listing two separate viewpoints of a topic. Topics can include anything that can be cleanly divided into two opposing views. For example, evaluating the pros and cons of a major decision is a common use of T-Charts. Other opposing views that work well include facts vs. opinions, advantages and disadvantages or strengths and weaknesses.

T-Chart

SPIDER MAPA Spider map(sometimes called a semantic map) is a type ofgraphic organizerthat is used to investigate and enumerate various aspects of a single theme or topic, helping the student to organize their thoughts. It looks a bit like a spider's web, hence its name.The process of creating a spider diagram helps the student focus on the topic, requires the student to review what they already know in order to organize that knowledge, and helps the student to monitor their growing comprehension of the topic. It also helps point out the areas where the student must investigate more (where the web is hard to fill out).If the topic at hand involves investigating attributes associated with a single topic, and then obtaining more details on each of these ideas, use a spider diagram as your graphic organizer. The spider diagram is like a star graphic organizer with another level of detail.For example, a spider diagram can be used to find methods that help your study skills (like taking notes, reading, memorizing, etc.), and investigate the factors involved in performing each of the methods.Another example is to use a spider map to prepare for a writing assignment; the student must concentrate on the main topic, list the big ideas concerning the topic, and think of the attributes/qualities/functions associated with each of these ideas.

SPIDER MAP

BRIDGING SNAPSHOTA graphic organizer is a visual tool that supports students by organizing ideas and structuring writing assignments. Sequence graphic organizers are designed to link actions or points in time for one or more characters or events. This method can be applied to a section of text, a chapter, or an entire story. Providing a linear perspective, sequence graphic organizers give the student a visual description of the topic's progression. Through this mapped process, students will be more capable of problem solving and developing ideas and opinions about a story line.

BRIDGING SNAPSHOT

SYNECTICSSynecticsis a group creativeproblem solvingprocess designed to increase the probability of successful solutions. The founding team originated in the Arthur D. Little Invention Design Unit in the 1950s, then set up Synectics Inc. (now Synecticsworld) in 1960to further explore and develop the Synectics process. The Synectics process was developed byGeorge M. Prince(April 5, 1918 - June 9, 2009)andWilliam J.J. Gordon, and today is taught, certified and practiced widely in business, industry, and education.

The Synectics process is designed to improve the probability of success in creative problem solving meetings by removing the negative elements of group human dynamics and replacing them with positive, collaborative tools to enable the team to focus their abilities on the challenge at hand. By employing positive group dynamic tools and a rigorous problem solving infrastrucure (guided by a facilitator) the team harnesses its multiplicative potential to problem solve.

The termSynecticsis derived from the Greek"Syn"and"Ectos"and means "the joining together of different and apparently irrelevant elements. History The Synectics team wanted to know what was really going on between members of a group when they were collaborating to creatively solve a problem. They began to tape-recorded (initially audio, later video) and deconstruct the interactions between the members of problem solving meetings. The Synectics team analyzed the group dynamics and methods of interacting and experiments with alternative ways of dealing with the obstacles to increase the probability of success in the meeting. "Success" was defined as getting a creative solution that the group was committed to implement. This history of sustained research and development provides a scientific foundation for the Synectics process, which continues to expand.Background Information: Synectics (Gordon, 1961) provides an approach to creative thinking that depends on looking at, what appears on the surface as, unrelated phenomenon and drawing relevant connections. Its main tools, analogies or metaphors. The approach, often used in groupwork, can help students develop creative responses to problem solving, to retain new information, to assist in generating writing, and to explore social and disciplinary problems. It helps users break existing minds sets and internalize abstract concepts. Synectics works well with all ages as well as those who withdraw from traditional methods (Couch, 1993).Teacher-facilitators use synectics in the classroom by leading students through a process which results in a three dimensional view of the "problem" in order to create solutions. Although this process appears a bit cumbersome, the resultant scope and depth of your options will justify the time spent.Remember, tools, when used for the right types of jobs hold great value; synectics does not work for every job. Define the word(s): Use a dictionary or other standard source to define each word, concept, or theme. I prefer an unabridged dictionary for more detailed definitions.To ensure a fresh view generate each of the following lists separately, put the current list away, and start the next list after a break of at least five to ten minutes. If time permits longer breaks yield more beneficial results.

When using synectics to define a person, appropriate for self evaluation, focus your questions on the areas ofphysical attributes, skills, interests, personality traits, attitudes, and emotional states. Create direct analogies:What words have the same or similar meaning?(use a Thesaurus or book of synonyms) Describe personal analogies:What would it feel like to have the characteristics or traits of? (describe emotions and physical attributes) Identify compressed conflicts:What words have the opposite meaning or characteristics?(use a book of antonyms) Create a new direct analogy:What words have the same or similar meaning?

Yes, this repeats the prompt from the second step. The difference, after going through the first three lists you will have gone deeper into the subject and this list will reflect that depth. Synthesis: Look at all four lists and find key words or phrases, expand on those to generate more. Finally, focus on a theme that may incorporate several elements based on the final list.

SYNECTICS

NETWORK TREEIn telecommunication networks, a tree network is a combination of two or morestar networks connected together. Each star network is a local area network (LAN) in which there is a central computer or server to which all theworkstationnodes is directly linked. The central computers of the star networks are connected to a main cable called thebus. Thus, a tree network is abus networkof star networks.

The illustration shows a tree network with five star networks connected to a common bus. The workstations are shown as small spheres, the central computers of the star networks are shown as larger spheres, connections within star networks are shown as short lines, and the bus is shown as a long, heavy line. The connections can consist of wire cables,optical fibercables, orwirelesslinks.

The tree networktopologyis ideal when the workstations are located in groups, with each group occupying a relatively small physical region. An example is a university campus in which each building has its own star network, and all the central computers are linked in a campus-wide system. It is easy to add or remove workstations from each star network. Entire star networks can be added to, or removed from, the bus. If the bus has low loss and/or is equipped withrepeaters, this topology can be used in a wide area network (WAN) configuration.

In a tree network, a cable failure in one of the star networks will isolate the workstation that it links to the central computer of that star network, but only that workstation will be isolated. All the other workstations will continue to function normally, except that they will not be able to communicate with the isolated workstation. If any workstation goes down, none of the other workstations will be affected. If a central computer goes down, the entire portion of the network served by it will suffer degraded performance or complete failure, but rest of the network will continue to function normally. If the bus is broken, serious network disruption may occur. If redundancy is needed, the central computers of the star networks can be interconnected in amesh networktopology.

NETWORK TREE

KWLHPredicting/EvaluatingUse to help students activate prior knowledge. It is a group instruction activity that serves as a model for active thinking during reading.K-Recall what groupKNOWs about the subject.W-Determine what groupWANTs to learn.L-Identify what groupLEARNed as they read.H -HOWwe can learn more

KWLH

MATRIX CHART

The matrix chart divides the screen into a grid. Rows represent the values in one text column (e.g., product line) and columns represent another text column (e.g., country). Each cell then shows a circle or bar that represents the value for its row/column combination (e.g., returns for golfing equipment for Belgium).Bars and BubblesThe two modes of the matrix, circles and bars, are useful in different situations. Bars, whose height represents numeric values, are better for exact comparisons and allow space for more columns. Circles, which show values via area, are good for showing non-negative values that vary greatly, and allow space for more rows. You can flip between the two modes in the "Expert Options" menu to the left of the visualizations.ColorsYou can display a third dimension of data using color. When you select a column to be represented by color, circles will turn into miniature pie charts and bars will be broken into differently-colored pieces. This option should be used with caution, since it's possible to create a cluttered display, but it can often be effective.Average, Total, and CountThe matrix chart automatically performs simple aggregation of the data set. For instance, if your data set has two rows that show returns for golfing equipment for Belgium, say $1,000 and $2,000 the grid cell for golfing eqipment/Belgium will aggregate these values. If you choose "Total" in the options pane, the value will be $3,000. Average would yield $1,500, and Count would show 2, the number of rows that correspond to that cell. Note that if your data set has no numeric columns, the only option is to aggregate by count.Size BySometimes you may wish to compare data within columns or rows. Use the "Size By" buttons to compare show proportions in individual columns, rows, or (if you use color) even within cells. MATRIX CHART

STAR WEB

Star webis aplay-by-mail gameof strategy and diplomacy invented in 1976 byRick Loomis. The game has won a number of awards over the years (including the 1984Charles S. Roberts AwardforBest Play-by-Mail Game,the 2000 and 2003Origins AwardsforBest Play-by-Mail Game,and the 1997 Origins Award forBest Ongoing Play-by-Mail Game), and is likely the longest lived play-by-mail game that started life in that medium. It remains a popular game atFlying Buffalo. Played for points,Starwebis primarily a hidden movementwargame. Six different types of players (Empire Builder, Merchant,Berserker, Apostle, Pirate, and Artifact Collector) gain points in different ways; nevertheless, most victories come from taking something away from somebody else.Players write down their orders using an arcane command language, which is then entered into theStarwebcomputer program and the orders calculated simultaneously. The results are then printed and mailed back to the players. In recent years the system has moved to e-mail. Scoring rules differ based on the character class. The game ends when any player reaches a score determined (but not revealed to the players) at the beginning of the game.One interesting concept in the game is the idea of "artifacts", a number of which are randomly scattered around the game map during setup. The artifacts have certain point values for each class, but the Artifact Collector gains considerably more points for holding collections of them in a single place. One of the artifacts, The Black Box, has a random effect which is not revealed to the players.Starwebuses the term "Berserker" with permission ofFred Saberhagen; Saberhagen returned the favor by using a fictionalizedStarwebgame as a backdrop for his novelOctagon(1981).In 1999Pyramidmagazine namedStarwebas one of theMillennium's Best. EditorScott Haringsaid "Starwebis the king of [play-by-mail games] -- the industry's most popular and longest running. ... Beautifully balanced, with a design so well-polished it gleams."

STAR WEB

CHAINAchainis a series of connectedlinkswhich are typically made of metal. A chain may consist of two or more links.Chains are usually made in one of two styles, according to their intended use: Those designed for lifting, such as when used with ahoist; for pulling; or for securing, such as with abicycle lock, have links that aretorusshaped, which make the chain flexible in twodimensions(The fixed third dimension being a chain's length.) Those designed for transferring power in machines have links designed to mesh with the teeth of thesprocketsof the machine, and are flexible in only one dimension. They are known asroller chains, though there are also non-roller chains such asblock chain.Two distinct chains can be connected using aquick linkwhich resembles a carabiner with a screw close rather than a latch.

CHAIN

SKETCHAsketch(ultimately fromGreek schedios, "done extempore") is a rapidly executed freehanddrawingthat is not usually intended as a finished work.A sketch may serve a number of purposes: it might record something that the artist sees, it might record or develop an idea for later use or it might be used as a quick way of graphically demonstrating an image, idea or principle. Sketching is generally prescribed part of studies of art studentsSketches can be made in any drawing medium. The term is most often applied to graphic work executed in a dry media such assilverpoint,graphite,pencil,charcoalorpastel. But it may also apply to drawings executed in pen and ink, ballpoint pen,water colourandoil paint. The latter two are generally referred to as "water colour sketches" and "oil sketches". A sculptor might model three-dimensional sketches inclay,plasticineor wax.The term "sketchbook" refers to a book of blank paper on which an artist can, (or has already) drawn sketches. The book might be purchased bound or might comprise loose leaves of sketches assembled or bound together.

Most visual artists use, to a greater or lesser degree, the sketch as a method of recording or working out ideas. The sketchbooks of some individual artists have become very well known,including those ofLeonardo da VinciandEdgar Degaswhich have become art objects in their own right, with many pages showing finishedstudiesas well as sketches.

The ability to quickly record impressions through sketching has found varied purposes in today's culture.Courtroom sketchesrecord scenes and individuals in law courts. Sketches drawn to help authorities find or identify wanted people are calledcomposite sketches.Street artistsin popular tourist areas sketch portraits within minutes. SKETCH

FISHBONEIshikawa diagrams(also calledfishbone diagrams,herringbone diagrams,cause-and-effect diagrams, orFishikawa) arecausal diagramscreated byKaoru Ishikawa(1968) that show thecausesof a specificevent.Common uses of the Ishikawa diagram areproduct designand quality defect prevention, to identify potential factors causing an overall effect. Each cause or reason for imperfection is a source of variation. Causes are usually grouped into major categories to identify these sources of variation. The categories typically include: People: Anyone involved with the process Methods: How the process is performed and the specific requirements for doing it, such as policies, procedures, rules, regulations and laws Machines: Any equipment, computers, tools, etc. required to accomplish the job Materials: Raw materials, parts, pens, paper, etc. used to produce the final product Measurements: Data generated from the process that are used to evaluate its quality Environment: The conditions, such as location, time, temperature, and culture in which the process operates

Ishikawa diagrams were popularized byKaoru Ishikawain the 1960s, who pioneered quality management processes in the Kawasakishipyards, and in the process became one of the founding fathers of modern management.The basic concept was first used in the 1920s, and is considered one of theseven basic toolsofquality control.It is known as a fishbone diagram because of its shape, similar to the side view of a fish skeleton.MazdaMotors famously used an Ishikawa diagram in the development of theMiatasports car, where the required result was "Jinba Ittai" (Horse and Rider as One). The main causes included such aspects as "touch" and "braking" with the lesser causes including highly granular factors such as "50/50 weight distribution" and "able to rest elbow on top of driver's door". Every factor identified in the diagram was included in the final design. FISHBONE

CYCLE GRAPH THEORYIncycle graph theory, there are two different types of object calledcycles; aclosed walkand asimple cycle. Aclosed walkconsists of a sequence ofverticesstarting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. Asimple cycle, also called acircleorpolygon, is a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex. Simple cycles may also be described by their sets of edges, unlike closed walks for which the multiset of edges does not unambiguously determine the vertex ordering. Acircuitcan be a closed walk allowing repetitions of vertices but not edges; however, the term is also sometimes used to describe a simple cycle, so explicit definition is recommended when it is used.

Adirected cyclein adirected graphis a sequence of vertices starting and ending at the same vertex such that, for each two consecutive vertices of the cycle, there exists an edge directed from the earlier vertex to the later one; the same distinction between closed walks and simple cycles may be made in the directed case.

CYCLE GRAPH THEORY

FLOWCHARTAflowchartis a type ofdiagramthat represents analgorithm, workflow or process, showing the steps as boxes of various kinds, and their order by connecting them with arrows. This diagrammatic representation illustrates a solution model to a givenproblem. Flowcharts are used in analyzing, designing, documenting or managing a process or program in various fields.

Flowcharts are used in designing and documenting complex processes or programs. Like other types of diagrams, they help visualize what is going on and thereby help the people to understand a process, and perhaps also find flaws, bottlenecks, and other less-obvious features within it. There are many different types of flowcharts, and each type has its own repertoire of boxes and notational conventions. The two most common types of boxes in a flowchart are: a processing step, usually calledactivity, and denoted as a rectangular box a decision, usually denoted as a diamond.A flowchart is described as "cross-functional" when the page is divided into differentswimlanesdescribing the control of different organizational units. A symbol appearing in a particular "lane" is within the control of that organizational unit. This technique allows the author to locate the responsibility for performing an action or making a decision correctly, showing the responsibility of each organizational unit for different parts of a single process.Flowcharts depict certain aspects of processes and they are usually complemented by other types of diagram. For instance,Kaoru Ishikawadefined the flowchart as one of the seven basic tools of quality control, next to thehistogram,Pareto chart,check sheet,control chart,cause-and-effect diagram, and thescatter diagram. Similarly, inUML, a standard concept-modeling notation used in software development, theactivity diagram, which is a type of flowchart, is just one of many different diagram types.

FLOWCHART

CEREBRAL CHART

GANNT CHARTAGantt chartis a type ofbar chart, developed byHenry Ganttin the 1910s, that illustrates aproject schedule. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of aproject. Terminal elements and summary elements comprise thework breakdown structureof the project. Modern Gantt charts also show thedependency (i.e., precedence network) relationships between activities. Gantt charts can be used to show current schedule status using percent-complete shadings and a vertical "TODAY" line as shown here.

Although now regarded as a common charting technique, Gantt charts were considered revolutionary when first introduced. This chart is also used ininformation technologyto represent data that have been collected.

Gantt charts can be used for scheduling generic resources, so as well as their use in project management, they can also be used inscheduling production processesandemployee rostering.In the latter context, they may also be known astimebar schedules.There are many computer applications supporting the use of Gantt charts foremployee scheduling. Gantt charts can be used to track shifts or tasks and also vacations or other types of out-of-office time.

GANNT CHART

EVALUATIVE PYRAMIDThe Pyramid of Evidence: A Useful Construct?Traditionally, the design of a study has been considered a principal barometer of the validity of its findings. In this construct, different study designs are considered in the context of a pyramid of evidence, in which studies most susceptible to threats to internal validity reside at the bottom and those least prone reside at the top.

This hierarchy is widely used in discussions about the quality of medical studies and is integrated into the grading of evidence in practice guidelines.However, although the pyramid of evidence is undoubtedly well suited for questions of therapeutic efficacy, it is of limited to no value for many other questions addressed in the medical literature, such as the effectiveness of therapies (ie, how well a treatment works in practice); the association between exposures that cannot be controlled and outcomes; or the safety or harm of a therapy or intervention. For some questions, RCTs are not feasible or are simply impossible. When RCTs are not available to answer a given question in a specific population, which is frequently the case, readers of the medical literature must determine the extent to which the study design implemented was appropriate for the question asked rather than implementing rigid constructs of study quality.

EVALUATIVE PYRAMID

CONCEPT MAPA concept map is a way of representing relationships betweenideas,images, orwordsin the same way that adiagram represents the grammar of a sentence, a road map represents the locations of highways and towns, and acircuit diagramrepresents the workings of an electrical appliance. In a concept map, each word or phrase connects to another, and links back to the original idea, word, or phrase. Concept maps are a way to develop logical thinking and study skills by revealing connections and helping students see how individual ideas form a larger whole. An example of the use of concept maps is provided in the context of learning about types of fuel. Concept maps were developed to enhance meaningful learning in the sciences. A well-made concept map grows within acontext framedefined by an explicit "focus question", while amind mapoften has only branches radiating out from a central picture. Some research evidence suggests that the brain stores knowledge as productions (situation-response conditionals) that act ondeclarative memorycontent, which is also referred to as chunks or propositions.Because concept maps are constructed to reflect organization of the declarative memory system, they facilitate sense-making and meaningful learning on the part of individuals who make concept maps and those who use themConcept maps are rather similar to topic maps in that both allow to connect concepts or topics viagraphs. Among the various schema and techniques for visualizing ideas, processes, and organizations, concept mapping, as developed byJoseph Novakis unique in its philosophical basis, which "makes concepts, and propositions composed of concepts, the central elements in the structure of knowledge and construction of meaning

CONCEPT MAP

BAR GRAPHAbar chartorbar graphis achartwithrectangularbars withlengthsproportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column bar chart. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulate effect (stacked bar graphs). Bar graph can be drawn horizontally or vertically.Bar charts have a discrete range. Bar charts are usually scaled so that all the data can fit on the chart. Bars on the chart may be arranged in any order. Bar charts arranged from highest to lowest incidence are called Pareto charts. Normally, bars showing frequency will be arranged in chronological (time) sequence. Grouped bar graph usually present the information in the same order in each grouping. Stacked bar graphs present the information in the same sequence on each bar.Bar graphs charts provide a visual presentation of categorical data.[1]Categorical data is a grouping of data into discrete groups, such as months of the year, age group, shoe sizes, and animals. These categories are usually qualitative. In a column bar chart, the categories appear along the horizontal axis; the height of the bar corresponds to the value of each category.Bar graphs can also be used for more complex comparisons of data with grouped bar charts and stacked bar charts.[1]In a grouped bar chart, for each categorical group there are two or more bars. These bars are color-coded to represent a particular grouping. For, a business owner with two stores might make a grouped bar chart with different colored bars to represent each store: the horizontal axis would show the months of the year and the vertical axis would show the revenue. Alternatively, a stacked bar chart could be used. The stacked bar chart stacks bars that represent different groups on top of each other. The height of the resulting bar shows the combined result of the groups. However, stacked bar charts are not suited to datasets where some groups have negative values. In such cases, grouped bar charts are preferable. BAR GRAPH

LINE GRAPHAline chartorline graphis a type ofchartwhich displays information as a series of data points called 'markers' connected by straight-linesegments.It is a basic type ofchartcommon in many fields. It is similar to ascatter plotexcept that the measurement points are ordered (typically by their x-axis value) and joined with straight line segments.Line Charts show how a particular data changes at equal intervals of time. A line chart is often used to visualize a trend in data over intervals of time atime series thus the line is often drawn chronologically

The name line graph comes from a paper byHarary & Norman (1960) although bothWhitney (1932) andKrausz (1943) used the construction before this.Other terms used for the line graph include thetheta-obrazom, thecovering graph, thederivative, theedge-to-vertex dual, theconjugate, and therepresentative graph,as well as theedge graph, theinterchange graph, theadjoint graph, and thederived graph. Hassler Whitney(1932) proved that with one exceptional case the structure of aconnected graphGcan be recovered completely from its line graph.Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs areclaw-free, and the line graphs ofbipartite graphsareperfect. Line graphs can be characterized by nineforbidden subgraphs, and can be recognized inlinear time.Various generalizations of line graphs have also been studied, including the line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs.

LINE GRAPH

PIE GRAPHA pie chart is a divided intosectors, illustrating numerical proportion. In a pie chart, thearc lengthof each sector (and consequently itscentral angleandarea), isproportionalto the quantity it represents. While it is named for its resemblance to apiewhich has been sliced, there are variations on the way it can be presented. The earliest known pie chart is generally credited toWilliam Playfair'sStatistical Breviaryof 1801.

Pie charts are very widely used in the business world and the mass media.However, they have been criticized,and many experts recommend avoiding them,pointing out that research has shown it is difficult to compare different sections of a given pie chart, or to compare data across different pie charts. Pie charts can be replaced in most cases by other plots such as thebar chart.

Statisticiansgenerally regard pie charts as a poor method of displaying information, and they are uncommon in scientific literature. One reason is that it is more difficult for comparisons to be made between the size of items in a chart when area is used instead of length and when different items are shown as different shapes.