TOPOLOGY
branch of mathematics concerned with the study of the properties of figures (or spaces) that are preserved under continuous deformations, such as stretching, compression, or bending. Continuous deformation is a deformation of a figure in which there are no breaks (i.e., violation of the integrity of the figure) or gluing (i.e., identification of its points). Such geometric properties are associated with the position, and not with the shape or size of the figure. Unlike Euclidean and Riemannian geometries, Lobachevsky geometry and other geometries that deal with the measurement of lengths and angles, topology has a non-metric and qualitative character. Previously, it was called “situs analysis” (position analysis), as well as “point set theory”. In popular science literature, topology is often called "rubber sheet geometry" because it can be visualized as the geometry of shapes drawn on perfectly elastic rubber sheets that are subjected to tension, compression, or bending. Topology is one of newest sections mathematics.
Story. In 1640, the French mathematician R. Descartes (1596-1650) found an invariant relationship between the number of vertices, edges and faces of simple polyhedra. Descartes expressed this relationship with the formula V - E + F = 2, where V is the number of vertices, E is the number of edges and F is the number of faces. In 1752, the Swiss mathematician L. Euler (1707-1783) gave a rigorous proof of this formula. Another contribution of Euler to the development of topology was the solution of the famous problem of the Königsberg bridges. It was about an island on the Pregel River in Koenigsberg (at the place where the river divides into two branches - Old and New Pregel) and seven bridges connecting the island with the banks. The task was to find out whether it was possible to walk around all seven bridges along a continuous route, visiting each one only once and returning to the starting point. Euler replaced land masses with dots and bridges with lines. Euler called the resulting configuration a graph, the points as its vertices, and the lines as its edges. He divided vertices into even and odd, depending on whether the number of edges leaving the vertex was even or odd. Euler showed that all the edges of a graph can be traversed exactly once along a continuous closed route only if the graph contains only even vertices. Since the graph in the Königsberg bridges problem contains only odd vertices, it is impossible to walk around the bridges along a continuous route, visiting each one exactly once and returning to the beginning of the route. The solution to the problem of the Königsberg bridges proposed by Euler depends only on the relative position of the bridges. It marked the formal beginning of topology as a branch of mathematics. K. Gauss (1777-1855) created the theory of knots, which was later studied by I. Listing (1808-1882), P. Tate (1831-1901) and J. Alexander. In 1840, A. Moebius (1790-1868) formulated the so-called four-color problem, which was subsequently studied by O. de Morgan (1806-1871) and A. Cayley (1821-1895). The first systematic work on topology was Listing's Preliminary Studies on Topology (1874). Founders modern topology
are G. Cantor (1845-1918), A. Poincaré (1854-1912) and L. Brouwer (1881-1966). Topology sections. Topology can be divided into three areas: 1) combinatorial topology, which studies by breaking them down into simple figures, regularly adjacent to each other; 2) algebraic topology, which deals with the study of algebraic structures associated with topological spaces, with an emphasis on group theory; 3) set-theoretic topology, which studies sets as clusters of points (in contrast to combinatorial methods, which represent an object as a union of more simple objects) and describing sets in terms of such topological properties as openness, closedness, connectedness, etc. Of course, this division of topology into regions is somewhat arbitrary; many topologists prefer to distinguish other sections in it.
Some basic concepts. A topological space consists of a set of points S and a set S of subsets of the set S satisfying the following axioms: (1) the entire set S and the empty set belong to the set S; (2) the union of any collection of sets from S is a set from S; (3) intersection of any finite number of sets from S is a set from S. The sets included in a set S are called open sets, and this set itself is called a topology in S.
See SET THEORY. A topological transformation, or homeomorphism, of one geometric figure S onto another, S", is a mapping (p (r) p") of points p from S to points p" from S", satisfying the following conditions: 1) the correspondence it establishes between points from S and S" are one-to-one, i.e. each point p from S corresponds to only one point p" from S" and to each point p" only one point p is mapped; 2) the mapping is mutually continuous (continuous in both directions), i.e. if two points p, q from S are given and point p moves so that the distance between it and point q tends to zero, then the distance between the corresponding points p, q" from S" also tends to zero, and vice versa. Geometric figures, transforming into each other under topological transformations are called homeomorphic. The circle and the boundary of a square are homeomorphic, since they can be transformed into each other by a topological transformation (i.e., bending and stretching without breaking or gluing, for example, stretching the border of a square onto a circle circumscribed around it). ).The sphere and the surface of the cube are also homeomorphic. To prove that the figures are homeomorphic, it is enough to indicate the corresponding transformation, but the fact that we cannot find a transformation for some figures does not prove that these figures are not homeomorphic.

Rice. 1. THE SURFACE OF THE CUBE AND THE SPHERE are homeomorphic, i.e. can be converted into each other by a topological transformation, but neither the surface of the cube nor the sphere is homeomorphic to the torus (the “donut” surface).

Topological property (or topological invariant) geometric shapes is a property that, along with a given figure, is also possessed by any figure into which it transforms during a topological transformation. Any open connected set containing at least one point is called a region. A region in which any closed simple (i.e., homeomorphic to a circle) curve can be contracted to a point while remaining in this region all the time is called simply connected, and the corresponding property of the region is simply connected. If some closed simple curve of this region cannot be contracted to a point, remaining all the time in this region, then the region is called multiply connected, and the corresponding property of the region is called multiply connected. Imagine two circular areas, or disks, one without holes and one with holes. The first region is simply connected, the second is multiply connected. Simply connected and multiply connected are topological properties. A region with a hole cannot go under homeomorphism to a region without holes. It is interesting to note that if in a multiply connected disk a cut is drawn from each of the holes to the edge of the disk, then it becomes simply connected. The maximum number of closed simple disjoint curves along which a closed surface can be cut without dividing it into separate parts is called the genus of the surface. Genus is a topological invariant of a surface. It can be proven that the genus of the sphere equal to zero, the genus of a torus (a donut surface) is one, the genus of a pretzel (a torus with two holes) is two, the genus of a surface with p holes is equal to p. It follows that neither the surface of a cube nor the sphere is homeomorphic to a torus. Among the topological invariants of a surface, one can also note the number of sides and the number of edges. The disk has 2 sides, 1 edge and genus 0. The torus has 2 sides, has no edges, and its genus is 1. The concepts introduced above allow us to clarify the definition of topology: topology is the branch of mathematics that studies properties that are preserved under homeomorphisms.
Important issues and results. Jordan's closed curve theorem. If a simple closed curve is drawn on a surface, is there any property of the curve that is preserved when the surface is deformed? The existence of such a property follows from the following theorem: a simple closed curve on a plane divides the plane into two regions, internal and external. This seemingly trivial theorem is obvious for curves simple type, for example, for a circle; however, for complex closed polylines the situation is different. The theorem was first formulated and proven by C. Jordan (1838-1922); however, Jordan's proof turned out to be wrong. A satisfactory proof was proposed by O. Veblen (1880-1960) in 1905.
Brouwer's fixed point theorem. Let D be a closed region consisting of a circle and its interior. Brouwer's theorem states that for any continuous transformation transforming every point of domain D to a point in the same domain, there is a certain point that remains fixed during this transformation. (The transformation is not assumed to be one-to-one.) Brouwer's fixed point theorem is of particular interest because it appears to be the most frequently used topological theorem in other branches of mathematics.
The problem of four colors. The problem is this: can any map be colored in four colors so that any two countries having common border, were painted in different colors? The four-color problem is topological, since neither the shape of countries nor the configuration of borders matters. The hypothesis that four colors are sufficient to properly color any map was first put forward in 1852. Experience showed that four colors were indeed sufficient, but a rigorous mathematical proof could not be obtained for more than a hundred years. It was only in 1976 that K. Appel and W. Haken from the University of Illinois, spending more than 1000 hours of computer time, achieved success.
One-sided surfaces. The simplest one-sided surface is the Möbius strip, named after A. Möbius, who discovered its extraordinary topological properties in 1858. Let ABCD (Fig. 2a) be a rectangular strip of paper. If you glue point A with point B, and point C with point D (Fig. 2, b), you will get a ring with an inner surface, an outer surface and two edges. One side of the ring (Fig. 2, b) can be painted. The painted surface will be limited to the edges of the ring. The beetle can travel around the world in a ring, remaining on either a painted or unpainted surface. But if, before gluing the ends, twist the strip half a turn and glue point A to point C, and B to D, then you get a Möbius strip (Fig. 2c). This figure has only one surface and one edge. Any attempt to color only one side of the Mobius strip is doomed to failure, since the Mobius strip only has one side. A beetle crawling along the middle of a Mobius strip (without crossing the edges) will return to its starting point in an upside-down position. When cutting a Mobius strip along the midline, it does not split into two parts.

Knots. A knot can be thought of as a tangled piece of thin rope with connected ends located in space. The simplest example- make a loop from a piece of rope, pass one of its ends through the loop and connect the ends. As a result, we get a closed curve that remains topologically the same, no matter how we stretch or twist it, without tearing or gluing individual points together. The problem of classifying nodes according to a system of topological invariants has not yet been solved.
LITERATURE
Hu Si-chiang. Homotopy theory. M., 1964 Kuratovsky A. Topology, vol. 1-2. M., 1966, 1969 Spenier E. Algebraic topology. M., 1971 Alexandrov P.S. Introduction to set theory and general topology. M., 1977 Kelly J. General topology. M., 1981

Collier's Encyclopedia. - Open Society. 2000 .

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Topology… Spelling dictionary-reference book

topology- Physical or logical distribution of network nodes. Physical topology defines the physical connections (links) between nodes. Logical topology describes possible connections between network nodes. In local networks, the three most common... ... Technical Translator's Guide

In a broad sense, the area of ​​mathematics that studies topology. properties decomp. math. and physical objects. Intuitively, to topological These include high-quality, stable properties that do not change with deformation. Math. formalization of the idea of ​​topological properties... ... Physical encyclopedia

Science, the study of localities. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. topology (gr. topos place, terrain + ...logy) a branch of mathematics that studies the most general properties of geometric figures (properties, not ... ... Dictionary of foreign words of the Russian language

TOPOLOGY, a branch of mathematics that studies the properties of geometric figures that remain unchanged under any deformation: squeezing, stretching, twisting (but without breaking or gluing). A cup with a handle is topologically equivalent to a donut; cube,... ... Scientific and technical encyclopedic dictionary

- (from the Greek topos place and...logy) a branch of mathematics that studies the topological properties of figures, i.e. properties that do not change under any deformations produced without breaks and gluing (more precisely, under one-to-one and continuous... ... Big Encyclopedic Dictionary

TOPOLOGY, topologies, many. no, female (from Greek topos place and logos teaching) (mat.). Part of geometry that studies the qualitative properties of figures (i.e., independent of concepts such as length, angles, straightness, etc.). Dictionary… … Ushakov's Explanatory Dictionary

The term topology describes the physical arrangement of computers, cables, and other network components.

Topology is a standard term used by professionals to describe the basic layout of a network.

In addition to the term “topology”, the following is also used to describe the physical layout:

Physical location;

Layout;

Diagram;

The network topology determines its characteristics. In particular, the choice of a particular topology affects:

composition of the necessary network equipment;

characteristics of network equipment;

network expansion possibilities;

network management method.

To share resources or perform other network tasks, computers must be connected to each other. For this purpose, in most cases, a cable is used (less commonly, wireless networks - infrared equipment). However, simply connecting your computer to a cable that connects other computers is not enough. Different types of cables, combined with different network cards, network operating systems, and other components, require different computer layouts.

Each network topology imposes a number of conditions. For example, it can dictate not only the type of cable, but also the way it is laid.

Basic topologies

• star

  ring

If computers are connected along a single cable, the topology is called a bus. When computers are connected to cable segments originating from a single point, or hub, the topology is called a star topology. If the cable to which the computers are connected is closed in a ring, this topology is called a ring.

Tire.

The bus topology is often called a “linear bus”. This topology is one of the simplest and most widespread topologies. It uses a single cable, called a backbone or segment, along which all computers on the network are connected.

In a network with a bus topology, computers address data to a specific computer by transmitting it along a cable in the form of electrical signals.

Data in the form of electrical signals is transmitted to all computers on the network; however, the information is received by the one whose address matches the recipient address encrypted in these signals. Moreover, at any given time, only one computer can transmit.

Since data is transmitted to the network by only one computer, its performance depends on the number of computers connected to the bus. The more there are, the slower the network works. The bus is a passive topology. This means that computers only “listen” to data transmitted over the network, but do not move it from sender to recipient. Therefore, if one of the computers fails, it will not affect the operation of the others. In this topology, data is distributed throughout the network - from one end of the cable to the other. If no action is taken, the signals reaching the end of the cable will be reflected and this will not allow other computers to transmit. Therefore, after the data reaches the destination, the electrical signals must be extinguished. To do this, terminators (also called plugs) are installed at each end of the cable in a network with a bus topology to absorb electrical signals.

Advantages: the absence of additional active equipment (for example repeaters) makes such networks simple and inexpensive.

Linear local network topology diagram

However, the disadvantage of a linear topology is the limitations on network size, functionality and expandability.

Ring

In a ring topology, each workstation is connected to its two closest neighbors. This relationship forms a local network in the form of a loop or ring. Data is transmitted in a circle in one direction, and each station plays the role of a repeater, which receives and responds to packets addressed to it and transmits other packets to the next one. workstation"down". In the original ring network, all objects were connected to each other. This connection had to be closed. Unlike the passive bus topology, here each computer acts as a repeater, amplifying signals and transmitting them next computer. The advantage of this topology was the predictable response time of the network. The more devices were in the ring, the longer the network took to respond to requests. Its most significant drawback is that if at least one device fails, the entire network refuses to function.

One of the principles of data transmission over a ring is called passing the token. The gist of it is this. The token is transmitted sequentially, from one computer to another, until the one that wants to transfer the data receives it. The sending computer modifies the token, places the email address in the data, and sends it around the ring.

This topology can be improved by connecting all network devices via hub(Hub device connecting other devices). Visually, a “tweaked” ring is no longer physically a ring, but in such a network data is still transmitted in a circle.

In the figure, solid lines indicate physical connections, and dotted lines indicate data transfer directions. Thus, such a network has a logical ring topology, while physically it is a star.

Star

In a star topology, all computers are connected using cable segments to central component having a hub. Signals from the transmitting computer travel through the hub to everyone else. In star networks, cabling and network configuration management are centralized. But there is also a drawback: since all computers are connected to a central point, cable consumption increases significantly for large networks. In addition, if the central component fails, the entire network will be disrupted.

Advantage: If one computer breaks down or the cable connecting one computer fails, then only that computer will not be able to receive and transmit signals. This will not affect other computers on the network. The overall network speed is limited only by the hub's bandwidth.

The star topology is dominant in modern local networks. Such networks are quite flexible, easily expandable and relatively inexpensive compared to more complex networks in which the methods of device access to the network are strictly fixed. Thus, “stars” have replaced outdated and rarely used linear and ring topologies. Moreover, they became a transitional link to the latter type topologies – dialed stars e.

A switch is a multiport active network device. The switch “remembers” the hardware (or MAC–MediaAccessControl) addresses of devices connected to it and creates temporary paths from the sender to the recipient, along which data is transmitted. In a typical local network with a switched topology, there are several connections to a switch. Each port and the device that is connected to it has its own bandwidth (data transfer rate).

Switches can significantly improve network performance. First, they increase the total bandwidth that is available for a given network. For example, an 8-wire switch can have 8 separate connections, supporting speeds of up to 10 Mbit/s each. Accordingly, the throughput of such a device is 80 Mbit/s. First of all, switches increase network performance by reducing the number of devices that can fill the entire bandwidth of a single segment. One such segment contains only two devices: the workstation network device and the switch port. Thus, only two devices can “compete” for a bandwidth of 10 Mbit/s, and not eight (when using an ordinary 8-port hub, which does not provide for such division of bandwidth into segments).

In conclusion, it should be said that topology is distinguished physical connections(physical structure of the network) and topology of logical connections (logical structure of the network)

Configuration physical connections is determined by the electrical connections of computers and can be represented as a graph, the nodes of which are computers and communications equipment, and the edges correspond to cable segments connecting pairs of nodes.

Logical connections represent the paths of passage information flows over the network, they are formed by appropriately configuring the communication equipment.

In some cases, the physical and logical topologies are the same, and sometimes they are not.

The network shown in the figure is an example of a mismatch between the physical and logical topology. Physically, computers are connected using a common bus topology. Access to the bus occurs not according to a random access algorithm, but by transferring a token (token) in a ring pattern: from computer A to computer B, from computer B to computer C, etc. Here, the order of token transfer no longer follows physical connections, but is determined by the logical configuration of network adapters. There is nothing stopping you from configuring network adapters and their drivers so that the computers form a ring in a different order, for example B, A, C... However, the physical structure does not change.

Wireless network.

The phrase “wireless environment” can be misleading because it means that there are no wires on the network at all. In reality, wireless components typically interact with a network that uses cable as the transmission medium. Such a network with mixed components is called hybrid.

Depending on the technology, wireless networks can be divided into three types:

local area networks;

extended local area networks;

mobile networks (laptop computers).

Transfer methods:

infrared radiation;

• radio transmission in a narrow spectrum (single-frequency transmission);

  radio transmission in the scattered spectrum.

In addition to these methods of transmitting and receiving data, you can use mobile networks, packet radio connections, cellular networks and microwave data transmission systems.

Currently office network- This is not just connecting computers to each other. It is difficult to imagine a modern office without databases that store both the financial statements of the enterprise and personnel information. IN large networks, as a rule, for the purpose of database security and to increase the speed of access to them, separate servers are used to store databases. Also, now it is difficult to imagine a modern office without access to the Internet. Scheme option wireless network office is shown in the picture

So let's conclude: the future network must be carefully planned. To do this, you should answer the following questions:

Why do you need a network?

How many users will there be on your network?

How quickly will the network expand?

Does this network require Internet access?

Is centralized management of network users necessary?

After this, draw a rough diagram of the network on paper. You should not forget about the cost of the network.

As we have defined, topology is the most important factor improving overall network performance. Basic topologies can be used in any combination. It is important to understand that the strong and weak sides Each topology affects the desired network performance and is dependent on existing technologies. It is necessary to strike a balance between the actual location of the network (for example, in several buildings), the possibilities of using the cable, the path of its installation and even its type.

The local network - important element any modern enterprise, without which it is impossible to achieve maximum labor productivity. However, to take advantage of networking capabilities full power, you need to configure them correctly, also taking into account that the location of the connected computers will affect the performance of the LAN.

Topology concept

The topology of local computer networks is the location of workstations and nodes relative to each other and options for their connection. In fact, this is a LAN architecture. The placement of computers determines specifications network, and the choice of any type of topology will affect:

• Types and characteristics of network equipment.
• Reliability and scalability of LAN.
• Local network management method.

There are many such options for the location of working nodes and methods for connecting them, and their number increases in direct proportion to the increase in the number of connected computers. Basic topologies local networks- these are “star”, “tire” and “ring”.

Factors to consider when choosing a topology

Before you finally decide on the choice of topology, you need to take into account several features that affect the performance of the network. Based on them, you can select the most suitable topology, analyzing the advantages and disadvantages of each of them and correlating this data with the conditions available for installation.

• The functionality and serviceability of each of the workstations connected to the LAN. Some types of local network topologies depend entirely on this.
• Serviceability of equipment (routers, adapters, etc.). A breakdown of network equipment can either completely disrupt the operation of the LAN or stop the exchange of information with one computer.
• Reliability of the cable used. Damage to it disrupts the transmission and reception of data across the entire LAN or one segment of it.
• Cable length limitation. This factor is also important when choosing a topology. If there is not much cable available, you can choose an arrangement that will require less of it.

About the star topology

This type of workstation arrangement has a dedicated center - a server, to which all other computers are connected. It is through the server that data exchange processes take place. Therefore, its equipment must be more complex.

Advantages:

• The topology of local "star" networks compares favorably with others in the complete absence of conflicts in the LAN - this is achieved through centralized management.
• Failure of one of the nodes or damage to the cable will not have any effect on the network as a whole.
• Having only two subscribers, main and peripheral, allows you to simplify network equipment.
• A cluster of connection points within a small radius simplifies the process of network control and also improves its security by limiting access to unauthorized persons.

Flaws:

• Such a local network becomes completely inoperable in the event of a central server failure.
• The cost of a star is higher than other topologies, since much more cable is required.

Bus topology: simple and cheap

In this connection method, all workstations are connected to a single line - a coaxial cable, and data from one subscriber is sent to the others in half-duplex exchange mode. Local network topologies of this type require the presence of a special terminator at each end of the bus, without which the signal is distorted.

Advantages:

• All computers are equal.
• The ability to easily scale the network even while it is running.
• The failure of one node does not affect the others.
• Cable consumption is significantly reduced.

Flaws:

• Insufficient network reliability due to problems with cable connectors.
• Low performance due to the division of the channel between all subscribers.
• Difficulty in managing and detecting faults due to parallel connected adapters.
• The length of the communication line is limited, therefore these types of local network topologies are used only for a small number of computers.

Characteristics of the ring topology

This type of communication involves connecting a worker node with two others, data is received from one of them, and data is transmitted to the second. The main feature of this topology is that each terminal acts as a repeater, eliminating the possibility of signal attenuation on the LAN.

Advantages:

• Quickly create and configure this local network topology.
• Easy scaling, which, however, requires shutting down the network while installing a new node.
• A large number of possible subscribers.
• Resistance to overloads and absence of network conflicts.
• The ability to increase the network to enormous sizes by relaying the signal between computers.

Flaws:

• Unreliability of the network as a whole.
• Lack of resistance to cable damage, so a parallel backup line is usually provided.
• High cable consumption.

Types of local networks

The choice of local network topology should also be made based on the type of LAN available. The network can be represented by two models: peer-to-peer and hierarchical. They are not very different functionally, which allows you to switch from one to another if necessary. However, there are still a few differences between them.

As for the peer-to-peer model, its use is recommended in situations where the possibility of organizing large network is absent, but the creation of some kind of communication system is still necessary. It is recommended to create it only for Not large number computers. Centralized control communications are commonly used in various enterprises to monitor workstations.

Peer-to-peer network

This type of LAN implies equality of rights for each workstation, distributing data between them. Access to information stored on a node can be allowed or denied by its user. As a rule, in such cases, the bus topology of local computer networks will be most suitable.

A peer-to-peer network implies the availability of workstation resources to other users. This means the ability to edit a document on one computer while working on another, remotely print and launch applications.

Advantages of a peer-to-peer LAN type:

• Ease of implementation, installation and maintenance.
• Small financial costs. This model eliminates the need to purchase an expensive server.

Flaws:

• Network performance decreases in proportion to the increase in the number of connected worker nodes.
• Absent one system security.
• Availability of information: when you turn off your computer, the data on it will become inaccessible to others.
• There is no single information base.

Hierarchical model

The most commonly used local network topologies are based on this type of LAN. It is also called “client-server”. The essence of this model is that if there is a certain number of subscribers, there is one main element- server. This control computer stores all data and processes it.

Advantages:

• Excellent network performance.
• United reliable system security.
• One information base common to everyone.
• Simplified management of the entire network and its elements.

Flaws:

• The need to have a special personnel unit - an administrator who monitors and maintains the server.
• Large financial costs for the purchase of a main computer.

The most commonly used configuration (topology) of local computer network in the hierarchical model it is a “star”.

The choice of topology (layout of network equipment and workstations) is solely important point when organizing a local network. The chosen type of communication should ensure the most efficient and effective safe work LAN. It is also important to pay attention financial costs and opportunities for further network expansion. Find rational decision- a difficult task that is accomplished through careful analysis and a responsible approach. It is in this case that correctly selected local network topologies will ensure maximum performance of the entire LAN as a whole.

Computer network topology

One of the most important differences between different types networks is their topology.

Under topology usually understand the relative position of network nodes relative to each other. To network nodes in in this case include computers, hubs, switches, routers, access points, etc.

Topology is the configuration of physical connections between network nodes. Network characteristics depend on the type of topology installed. In particular, the choice of a particular topology affects:

• on the composition of the necessary network equipment;
• on the capabilities of network equipment;
• on the possibility of network expansion;
• on the way the network is managed.

The following main types of topologies are distinguished: shield, ring, star, mesh topology And lattice. The rest are combinations of basic topologies and are called mixed or hybrid.

Tire. Networks with a bus topology use a linear mono channel ( coaxial cable) data transmission, at the ends of which special plugs are installed - terminators. They are necessary in order to

Rice. 6.1.

to extinguish the signal after passing through the bus. To the disadvantages bus topology the following should be included:

• data transmitted via cable is available to all connected computers;
• If a bus fails, the entire network stops functioning.

Ring is a topology in which each computer is connected by communication lines to two others: from one it receives information, and to the other it transmits it and implies the following data transfer mechanism: data is transmitted sequentially from one computer to another until it reaches the recipient computer. The disadvantages of the ring topology are the same as those of the bus topology:

• public availability of data;
• instability to damage to the cable system.

Star is the only network topology with an explicitly designated center, called network hub or a “hub” to which all other subscribers are connected. The functionality of the network depends on the status of this hub. In a star topology, there are no direct connections between two computers on the network. Thanks to this, it is possible to solve the problem of public data availability, and also increases the resistance to damage to the cable system.

Rice. 6.2.

Rice. 6.3. Star topology

is a computer network topology in which each network workstation is connected to several workstations on the same network. It is characterized by high fault tolerance, complexity of configuration and excessive cable consumption. Each computer has many possible ways connections with other computers. A broken cable will not result in loss of connection between the two computers.

Rice. 6.4.

Lattice is a topology in which the nodes form a regular multidimensional lattice. In this case, each lattice edge is parallel to its axis and connects two adjacent nodes along this axis. A one-dimensional lattice is a chain connecting two external nodes (which have only one neighbor) through a number of internal nodes (which have two neighbors - on the left and on the right). By connecting both external nodes, a ring topology is obtained. Two- and three-dimensional lattices are used in supercomputer architecture.

Networks based on FDDI use the " double ring", thereby achieving high reliability and performance. A multi-dimensional lattice connected cyclically in more than one dimension is called a "torus".

(Fig. 6.5) - a topology that prevails in large networks with arbitrary connections between computers. In such networks, it is possible to identify individual randomly connected fragments ( subnets ), having a standard topology, therefore they are called networks with mixed topology.

To connect a large number of network nodes, network amplifiers and (or) switches are used. Active hubs are also used - switches that simultaneously have amplifier functions. In practice, two types of active hubs are used, providing the connection of 8 or 16 lines.

Rice. 6.5.

Another type of switching device is a passive hub, which allows you to organize a network branch for three workstations. The low number of connectable nodes means that a passive hub does not require an amplifier. Such concentrators are used in cases where the distance to the workstation does not exceed several tens of meters.

Compared to a bus or ring, a mixed topology is more reliable. The failure of one of the network components in most cases does not affect the overall performance of the network.

The local network topologies discussed above are basic, i.e. basic. Real computer networks are built based on the tasks that a given local network is designed to solve, and on the structure of its information flows. Thus, in practice the topology computer networks is a synthesis of traditional types of topologies.

Main characteristics of modern computer networks

The quality of network operation is characterized by the following properties: performance, reliability, compatibility, manageability, security, extensibility and scalability.

To the main characteristics productivity networks include:

• reaction time – a characteristic that is defined as the time between the occurrence of a request to any network service and receiving a response to it;
• throughput – a characteristic that reflects the amount of data transmitted by the network per unit of time;
• transmission delay – the interval between the moment a packet arrives at the input of any network device and the moment of its appearance at the output of this device.

For reliability assessments networks are used various characteristics, including:

• availability factor, meaning the proportion of time during which the system can be used;
• safety, those. the ability of the system to protect data from unauthorized access;
• fault tolerance - the ability of a system to operate under conditions of failure of some of its elements.

Extensibility means it can be added relatively easily individual elements networks (users, computers, applications, services), increasing the length of network segments and replacing existing equipment with more powerful ones.

Scalability means that the network allows you to increase the number of nodes and the length of connections within a very wide range, while the network performance does not deteriorate.

Transparency – the ability of a network to hide details of its internal structure, thereby simplifying its work on the network.

Controllability network implies the ability to centrally monitor the status of the main elements of the network, identify and resolve problems that arise during network operation, perform performance analysis and plan network development.

Compatibility means that the network is capable of incorporating a wide variety of software and hardware.

Topology- a rather beautiful, sonorous word, very popular in some non-mathematical circles, interested me back in the 9th grade. Of course, I didn’t have an exact idea, however, I suspected that everything was tied to geometry.

The words and text were selected in such a way that everything was “intuitively clear.” The result is a complete lack of mathematical literacy.

What is topology ? I’ll say right away that there are at least two terms “Topology” - one of them simply denotes a certain mathematical structure, the second one carries with it a whole science. This science consists of studying the properties of an object that will not change when it is deformed.

Illustrative example 1. Bagel cup.

We see that the mug, through continuous deformations, turns into a donut (in common parlance, a “two-dimensional torus”). It was noted that topology studies what remains unchanged under such deformations. In this case, the number of “holes” in the object remains unchanged - there is only one. For now we’ll leave it as it is, we’ll figure it out a little later)

Illustrative example 2. Topological man.

By continuous deformations, a person (see picture) can unravel his fingers - a fact. It's not immediately obvious, but you can guess. But if our topological man had the foresight to put a watch on one hand, then our task will become impossible.

Let's be clear

So, I hope a couple of examples brought some clarity to what is happening.
Let's try to formalize all this in a childish way.
We will assume that we are working with plasticine figures, and plasticine can stretch, compress, while gluing different points and tearing are prohibited. Homeomorphic are figures that are transformed into each other by continuous deformations described a little earlier.

A very useful case is a sphere with handles. A sphere can have 0 handles - then it’s just a sphere, maybe one - then it’s a donut (in common parlance, a “two-dimensional torus”), etc.
So why does a sphere with handles stand out among other figures? Everything is very simple - any figure is homeomorphic to a sphere with a certain number of handles. That is, in essence, we have nothing else O_o Any three-dimensional object is structured like a sphere with a certain number of handles. Be it a cup, spoon, fork (spoon=fork!), computer mouse, Human.

This is a fairly meaningful theorem that has been proven. Not by us and not now. More precisely, it has been proven for much more general situation. Let me explain: we limited ourselves to considering figures molded from plasticine and without cavities. This entails the following troubles:
1) we can’t get a non-orientable surface (Klein bottle, Möbius strip, projective plane),
2) we limit ourselves to two-dimensional surfaces (n/a: sphere - two-dimensional surface),
3) we cannot obtain surfaces, figures extending to infinity (of course we can imagine this, but no amount of plasticine will be enough).

The Mobius strip

Klein bottle