Link-level Network Topology GenerationMehmet Burak Akgun and Mehmet Hadi Gunes

Department of Computer Science and Engineering, University of Nevada, RenoEmail: {makgun, mgunes}@cse.unr.edu

Abstract—Internet topology generation involves producing syn-thetic network topologies that imitate the characteristics of theInternet. Although the accuracy of newly developed networkprotocols or algorithms do not considerably depend on theunderlying topology, the performance generally depends on thetopology. As a result, synthetic topologies are widely utilized bynetwork researchers to analyze performance of their design insimulation or emulation environments. Previous studies on theInternet topology generation have ignored the major buildingblock of the networks, i.e., subnetworks. Generated topologiesare composed of point to point links. These networks do notref ect some crucial characteristics of the Internet such as theclustering of the Internet backbone. In this study, we proposesubnet based Internet topology generation to better ref ect theunderlying building blocks of the Internet. Subnet based synthetictopologies capture both the degree distribution and the subnetdistribution characteristics of sample Internet topologies.

Keywords-Internet, subnetworks, topology generation

I. INTRODUCTION

Internet, the largest man made complex network, is a webof interconnected backbone networks over which thousands ofsmall and medium size Autonomous Systems (ASes) connectindividuals, businesses, universities, and agencies. Internetis a spontaneously growing complex system whose large-scale structure is affected by many interacting units aimed atoptimizing local communication eff ciency without a centralauthority. Due to the tremendous growth in Internet’s im-portance, many groups, organizations, and governments havebecome interested in understanding various characteristics ofthe Internet for commercial, social, and technical reasons. Theresearch community has been conducting numerous Internetmeasurement studies to understand the functional and topo-logical characteristics of the Internet. Depending on the natureof measurement study, researchers may use different types oftopology maps including AS level [1], [2], Point-of-Presencelevel [3], router level [4], [5], link level [6], [7] or IP addresslevel maps [8].Internet modeling mainly focuses on understanding local

and global characteristics of the Internet at AS, PoP, orrouter level, and construction of graph models that mimicthe observed topological characteristics. Generation of realisticInternet topologies is an important research problem [9],[10]. This understanding is especially important for newlydeveloped protocols as the performance of protocols highlydepend on the topological features of the Internet [11], [12],[13]. A protocol may perform very eff ciently on a model,but run quite poorly when deployed on the Internet. Hence,realistic sample network topology generation is highly valu-

able for many practitioners. If simulation is performed on non-representative topologies, then the results of the analysis wouldbe misleading.Previous studies on the Internet topology generation have

ignored the major building block of the networks, i.e., sub-networks. In general, generated topologies are composed ofpoint to point links ignoring multi-access links. Hence, thesenetworks do not ref ect some crucial characteristics of theInternet such as the degree distribution and clustering of theInternet backbone. In this study, we point the distinctionbetween real degree distribution (i.e., number of interfaces)and observed degree distribution(i.e., number of one hopneighbors). As subnets are the building blocks of networks,we propose subnet based Internet topology generation tobetter ref ect the underlying structure of the Internet. Subnetbased synthetic topologies capture both the degree distributionand the subnet distribution characteristics of sample Internettopologies, which are collected using the Cheleby InternetTopology Mapping System [14]. Subnet distribution ref ectsthe distribution of different subnet masks. This approachcaptures both hierarchical nature of the network deploymentand observed degree characteristics of the backbone.In the rest of the paper, we f rst present the related work on

Internet topology generation in Section II. In Section III, weindicate the need for the subnet-based topology generation.In Section IV, we present subnet based Internet topologygeneration. In Section V, we present sample results from ourexperiments. Finally, we conclude the paper in Section VI.

II. RELATED WORK ON TOPOLOGY GENERATION

Initially, network models relied on the traditional frame-works such as the Erdos−Renyi [15]. Despite the small-worldproperties in this model, it is not a good model for theInternet topologies due to its failure to reproduce many crucialproperties of the Internet such as the heavy tailed degreedistribution and the clustering coeff cient. Erdos-Renyi modelis extended to construct generalized random graphs with a pre-def ned degree distribution [16], [17]. However, these modelsare also far from representing the major structural propertiesof the Internet. Additionally, based on the fact that many socialnetworks are not only highly clustered but also have a smallaverage distance between nodes [18], Watts−Strogatz modelinterpolates between ordered lattices (with large clusteringcoeff cients) and purely random networks (with small averagepath lengths) [19]. However, empirical observations showedthat the model misses several important features such asthe degree distribution. Moreover, several topology generators

were based on the observed hierarchical structure of the Inter-net [20], [21]. Nonetheless, certain features of these generatorsprevent them from accurately modeling the Internet topology.Some network topology generators mimicked the network

deployment practices. For instance, Tiers [20] captures thehierarchical aspect of the Internet by implementing three levelsof hierarchy; WAN, MAN, LAN. In Tiers, a user can specifythe number of nodes in MAN/LAN levels of the hierarchywhere the nodes are linked by building minimum spanningtrees. Similarly, GT-ITM [22] generates hierarchical networksby building transit and stub domains. GT-ITM generates aconnected random graph in which each node is consideredas a transit domain. Each transit domain is then grown tocontain another connected random graph. After expanding op-eration for n-levels, a number of random graphs are generatedand connected to each node as stubs. Moreover, IGEN [23]implements heuristics implemented by Internet engineers topopulate networks based on some design choices.The milestone study by Faloutsos et al. pointed the power-

law degree characteristic of the Internet topologies at differentlevels [24]. Later, Govindan et al. indicated that the degreedistribution of the Internet is highly correlated with the idealpower law distribution [25]. These studies shifted the attentionto degree based generators. In order to bridge the gap betweenthe local and the global properties of the Internet, statisticalphysics based approaches are proposed [11], [26], [27]. Sincein most real-world networks new edges are not placed ran-domly but have a tendency to connect to high degree nodes,preferential attachment paradigm has been introduced [28].Attraction degree of nodes can be estimated based on theinternal and external factors such as the effects of attributeevolution and geographical limit on topology evolution [29].In this direction, BRITE [30] utilizes the preferential attach-ment model to generate power-law networks. BRITE allowslocality based preferential attachment to generate hierarchicalnetworks. BRITE also utilizes the Erdos-Renyi model in whichthe probability of existence of a link between two nodes isinversely proportional with the distance between the nodes.Similarly, Inet [31] produces graphs that have a power-lawdegree distributions by connecting nodes of pre-determineddegree.Similarly, the out-degree distribution of routers has shown

to exhibit Weibull distribution [32]. Hence, new topologygenerators have been developed to reproduce the observeddegree distributions [33], [34]. Jellyf sh model uses a coreformed around central nodes to obtain topologies that re-semble characteristics of the genuine samples [35]. Wealth-based Internet Topology generator captures high clusteringof the AS level topologies along with the scale-free degreedistribution [36].Another approach to topology generation is to generate

synthetic topologies that will capture major observed charac-teristics of sampled Internet topologies including assortativitycoeff cient, clustering, average shortest path and the smallestand largest eigenvalue of the Laplacian [2], [37]. In thistechnique, authors use dK-series as a basis to characterize

the graph of Internet measurements. For an n-node network0K-graph only matches the average degree, 1K-graph matchesthe degree distribution, 2K-graph matches the Joint DegreeDistribution and so on. The nK-graph is the isomorphic of theoriginal graph. Mahadevan et al. introduce a methodology forthe rescaling process to produce different sized graphs havingthe same dK-series characteristics [37]. Authors also argue that1K-graphs, i.e, only matching the degree distribution of routerlevel topologies, is not suff cient to preserve certain metrics.It should be noted that a given sample may not be repre-

sentative for all characteristics [38]. Lakhina et. al. indicatedthat, using (k,m)-traceroutes (i.e., traceroutes from k sourcesto m destinations where k≪m) introduces sampling bias intopology measurements [39]. Authors experimentally showthat using (k,m)-traceroute probes result in network topologieswith degree distributions following the power laws whereas thedegree distributions in the underlying original graphs do notnecessarily follow the power laws. Furthermore, the degreedistribution by itself is not suff cient to properly represent theInternet topology [40].In this paper, we advance network topology generation by

considering the subnetworks, i.e., the building blocks of thenetworks. Instead of only generating point-to-point links, thesubnet based topology generation considers the multi-accesslinks, which provide one hop connectivity to a set of nodes.Using subnets, we believe that one can better model theInternet topology.

III. MAKING THE CASE

Network topology generation involves producing synthetictopologies which imitate the characteristics of the Internet.Although the accuracy of newly developed network protocolsor algorithms do not generally depend on the underlyingtopology, the performance depends on the underlying net-work [30]. Hence, synthetic topologies are widely used bynetwork practitioners to analyze the performance of theirdesign in simulation environments before actual deployment.If the synthetic topology used during simulation does notrepresent the Internet topology, simulation results of the designwill be misleading and the expected performance will not beobserved when the system is deployed.Previous topology generators have ignored the subnet rela-

tion between routers while subnets are a major building blockof the network. Most topology generators produce networkscomposed of only point-to-point links. These topologies mis-represent the Internet as they ignore multi-access links, whichprovide one hop connectivity to a set of nodes and increasethe cliqueness of the topology. Therefore, subnets should beconsidered in generating network topologies in addition to theobserved power-law degree distribution of the Internet topol-ogy. For this, we obtain subnet and interface distributions frommeasurement studies to guide the synthetic topology genera-tion process. Our study emphasizes the distinction between theobserved degree distribution (i.e., sum of all routers connectedvia subnets) and real degree distribution (i.e., the number ofinterfaces). Accurately modeling the subnets helps us achieve

A B

C

A

A B&C

(a) Topology-1 (b) Topology-2 (c) Topology-3

Fig. 1. Sample Topologies

the hierarchical characteristics of network deployment alongwith the large-scale characteristics of the Internet.It is important to point the distinction between real and

observed degree of a router. Real degree of a router is thenumber of interfaces it is using to connect to neighboringsystems. Observed degree is the sum of all systems the routerhas one hop distance through a link, which can be a multiaccess link. For instance, observed degree distribution of f rsttwo topologies given in Figure 1 is exactly the same wherenode-A has a degree of 6. However node-A in Figure 1-(a) has 2 interfaces whereas the one in Figure 1-(b) has6. Hence, two topologies with exactly the same observeddegree distribution may actually have different real degree (i.e.,interface) distributions. (The comparison between Figure 1-(a) and Figure 1-(c) will be explained in the merging part ofthe procedure section.) The distinction between real degreeand observed degree is important. If we consider a routerconnected to 3 subnets of /24, it may have an observed degreeup to 762, i.e., 3*254 as the network address of 24 bits leaves8 bits for host addressing. However the real degree is 3 as itonly has 3 network interfaces.

IV. SUBNET-BASED NETWORK TOPOLOGY GENERATION

In the following, we discuss an approach to generate syn-thetic topologies which matches both the degree distributionand the subnet distribution of the Internet.There are two approaches to satisfy the distribution spec-

if cations. In the subnet centric approach, we f rst satisfysubnet distribution by generating subnets and then combinethe nodes belonging to different subnets to match the degreedistribution objective. Alternatively, in degree centric approachwe may f rst determine the degree distribution of nodes andthen iteratively link the nodes to satisfy the subnet distribution.Below, we provide an overview of the pseudo code for thesubnet centric approach.

A. InputDegree and subnet distribution data obtained from an Inter-

net measurement study such as the Cheleby Internet topologymapping system [14].In the rest of the paper, /i notation is used to represent

subnet masks and x is the set of all possible subnet masks.• SDref

i : The subnet frequency distribution for each subnet/i where i < 32. This parameter specif es the numberof subnets having a subnet mask of /i in the referencetopology, e.g., count values in Table I.

TABLE ISAMPLE SUBNET DISTRIBUTION

Count Completeness/24 4 26.38%/25 36 29.96%/26 184 28.30%/27 1,294 27.73%/28 8,836 27.96%/29 93,110 39.33%/30 20,543 100 %/31 37,468 100 %

• Crefi : The subnet completeness distribution for each

subnet /i where i < 32. This parameter specif es theutilization level of subnet IP addresses, e.g., completenessvalues in Table I.

• DDrefk : Observed degree distribution, i.e., the number of

routers with an observed degree of k for each possible k.• Aliasref : Average number of interfaces per router. Forinstance, for the sample data we used from Chelebysystem, the value is 2.61.

• r: The total number of routers in the reference network.For instance, it is 147.5K for the sample data fromCheleby system, as the total number of IP addresses, i.e.,385K is divided by the average number of interface perrouter, i.e., 2.61.

• n: User specif ed, desired number of nodes for the targettopology.

B. OutputA network topology of n nodes satisfying both the observed

degree distribution and the subnet distribution provided bymeasurements.

C. Procedure

Calculation of the desired subnet distribution: The num-ber of subnets at each subnet level is calculated by simplyscaling the data to the desired size. SDdesired

i = (n/r)SDrefi

∀i ∈ x.Creation of subnets: Create SDdesired

i subnets ∀i ∈ x.Calculation of the number of nodes to be attached to

each subnet: As the maximum number of nodes that can existin a subnet level i is 232−i − 2, we can f nd the desirednumber of nodes at each subnet level by multiplying withthe corresponding completeness value Cref

i . NSdesiredi =

(232−i − 2)Crefi ∀i ∈ x. A more precise alternative is to

use subnet size distribution given in Figure 2. Each curve

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80

Norm

alized

Frequency

of Subnets

Number of Nodes in the subnet

/24

/25

/26

/27

/28

/29

/3x

Fig. 2. Sample Subnet Size Distribution

1

10

100

1000

10000

100000

1000000

1 10 100 1000

Number of nodes

Node degree

Fig. 3. Sample Observed Degree Distribution

represents the size distribution of each subnet level. Note thateach curve is normalized with the maximum frequency in thecorresponding subnet level. Normalized histogram given in thef gure can simply be multiplied with the NSdesired

i to f ndthe distribution of the number of nodes to be attached at thecorresponding subnet level.Creation and attachment of nodes: Create NSdesired

i

nodes ∀i ∈ x and attach them to the corresponding subnet. Atthis stage, the desired subnet distribution is satisf ed. However,subnets are disconnected from each other and the n∗Aliasref

nodes exist in the network which need to be merged to obtainthe desired degree distribution and meet the target goal of nnodes.Calculation of the desired degree distribution: The char-

acteristic power law distribution is given as DDrefk = a∗k−q

where k is the node degree. Σ(DDrefk ) = Σ(a ∗ k−q) =

a∗Σ(k−q) = n. Hence, distribution for a different size with thesame power-law can be obtained by scaling the a parameter.DDdesired

k = (n/r)DDrefk . Figure 3 shows the observed de-

gree distribution of the sample topology from Cheleby Internettopology mapping system. Using the distribution in the f gure,k and q parameters of the best-f t curve is calculated. Figure 4illustrates the scaling process which simply shifts the curve

1

10

100

1000

10000

100000

1000000

1 10 100 1000

Number of Nodes

Node Degree

Upscale by 3

Best fit curve

Downscale by 0.2

Fig. 4. Degree Shift

upwards when n > r and downwards when n < r. Since thecurve itself is not linear, the maximum degree in the networkdo not scale linearly [37]. Note that, the summation of allvalues of the desired degree distribution curve equals n whilethat of the reference degree distribution curve equals r.Node merging to reach the target network size: Let kmax

be the maximum value of k(i.e., node degree) and kmin bethe minimum value of k such that DDdesired

k 6= 0. Fromkmax to kmin Merge(k,DDref

k ). AsDDdesiredk is calculated,

the merge function tries to converge to the desired degreedistribution by merging nodes. Merge operation combinestwo nodes, such that, the resulting node inherits the subnetsof both merged nodes and its degree is the sum of themerged nodes. For instance, Figure 1-(c) illustrates the mergeoperation. Node-B and Node-C in Figure 1-(a) is merged andthe resulting network is given in Figure 1-(c). Node-B has aninitial observed degree of 3 and node C has an initial degreeof 2, whereas the resulting node has an observed degree of 5and real degree of 2. Note that total number of nodes in thenetwork is decreased by one at each merge operation. Anotherimportant point about merging is that nodes which alreadyhave a common subnet should not be merged. After eachmerge function call, current degree distribution is recalculated

1

10

100

1000

10000

100000

1 10 100 1000

Number of Nodes

Node Degree

Desired Degree Distribution

Final Degree Distribution

Fig. 5. Matched Degree Distribution (100K node sample)

and compared with the desired one. The merge operationcontinues until desired distribution is matched. First round ofmerge function tries formation of DDdesired

kmax

nodes of degreekmax by merging existing nodes of highest possible degree.As the condition for kmax is satisf ed, the algorithm iteratesover all degrees k towards kmin.Overall, in subnet-centric approach, we utilize the subnet

characteristics of a reference Internet topology data to generatesubnets and attach network interfaces to the subnets based ontheir completenesses. Then, the merge operation determinesnetwork interfaces that will belong to the same router. Sincemerge operation does not connect or disconnect any interfacesfrom the generated subnets, it does not have any effect onthe subnet distribution. Hence, while the degree distributionconverges to the desired power-law distribution, the subnetdistribution is preserved.

V. RESULTS AND DISCUSSION

Modeling subnets in the process of Internet topology gen-eration helps capture many characteristics of the underlyingtopology. We generate topologies of any size matching boththe subnet distribution and the degree distribution. Figure 5presents the desired and f nal degree distribution of a 100Knode topology. In this sample, the resulting degree distribu-tion precisely follows the desired power law distribution. Inaddition to the observed degree and the subnet distributions,subnet size distribution and the average alias per node matchesthe reference topology.Figure 6 presents the alias distribution of the resulting

topology. Generating a power law distribution of observeddegree resulted in an alias distribution which matches thesample data for lower degrees but does not match for highervalues. This might be due to the bias caused by giving thepriority to the higher degree nodes than lower ones in themerging stage. On the other hand, giving higher priority tothe lower degree nodes may cause an inf ation in the aliasdistribution. Finding an optimum merging strategy is a futurework in addition to matching the interface distribution ofsample data.In the subnet creation stage, using only the completeness

value of the reference topology generates subnets of f xed

100

1000

10000

100000

1 10Number of nodes

Real Degree

Fig. 6. Resulting Alias Distribution (100K node sample)

size such that all subnets at the same subnet level havethe same number of nodes. This causes impulsive points inthe degree distribution of the network and makes it diff cultto achieve the desired power-law degree distribution in themerging stage since the size of subnets are not well distributed.However, using the subnet size distribution (as in Figure 2)helps generate f ne grained subnet sizes within the networkand also makes it easy to achieve a desired degree distribution.Although this study uses Cheleby Internet topology map-

ping system [14], the algorithm presented here is not de-pendent on the specif c data set. Other Internet topologymeasurement results can easily be ported as the referencetopology.

VI. CONCLUSION AND FUTURE WORK

Even though several topology generators exist, they lack tocapture a very important network feature, i.e., subnets. In thispaper, we emphasize the distinction between the observed de-gree distribution and the real degree distribution. The observeddegree distribution is inf ated due to the existence of multi-access links in the underlying topology. Hence, we producesynthetic topologies that match both the subnet distributionand the degree distribution. This results in interface distri-butions similar to the sample data. As future work, we willinvestigate approaches to improve the interface distribution.One method may be modifying the merge function to matchthe real degree distribution rather than the observed degree dis-tribution. Moreover, we will investigate approaches to matchother network characteristics such as graph density, averageshortest path and assortativity. For instance, assortativity is

affected by the merging strategy as merging similar degreenodes increases the assortativity. Finally, we will analyze thenode centric approach where we f rst generate nodes withpredef ned degrees and then converge them to the desiredsubnet distribution by merging the links.

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