Community Comparison in Communication Networks

Belkacem Serrour and Hamamache KheddouciUniversite de Lyon, Laboratoire LIESP, Bat. Nautibus,

43, Bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France{belkacem.serrour,hamamache.kheddouci}@univ-lyon1.fr

Abstract—If we draw the virtual topology representing thecommunication in networks, we observe that the structure issimilar to those of the social networks. Social networks arethese networks with the characteristic relating densely someentities than others. These dense zones are called communities.Generally, the members of a same community share the sameinterest. In this work, we look for which virtual topology (calledcommunication graph) emerged in communication networkgives communities closer to the real one. Three differentcommunication graphs are generated and compared with thegraph representing the real communities, the reference graph.Microscopic and macroscopic comparisons are done.

Keywords-Community detection, community comparison,communication networks.

I. INTRODUCTION

Many of the communication network protocols makeappeared a social network behavior [1][2]. If we draw thevirtual topology representing the communication in network,we obtain a graph structure similar to the social networksstructure. Social networks are these networks characterizedby some denser zones called communities. Let CG = (V,E)be a communication graph (links between communicatingpeers), where V represents the peers of the network and eachedge of E between two peers represents the communicationbetween them. In this work, we look for which kind ofcommunication graph (so, which network) is closer to thereal one (reference graph). The reference graph is the socialnetwork extracted from the network. It represents the realcommunities of interest issued in a given network. The aim isto find which communication graph is close to that referenceone. We model the networks by graphs, we extract fromthem the reference graphs, we generate from the graphsseveral communication graphs based on the communicationprotocol taken, we use one community detection algorithmto detect communities in each graph and finally, we comparethe communities of each communication graph with thecommunities of the reference graph.

II. COMMUNICATION GRAPHS AND COMMUNITYCOMPARISON

Our study starts with a network. We generate the networksby varying some parameters. The taken parameters are: nnetwork size (number of peers in the network), e networkdensity (number of links between nodes), s number ofservers in the network, r number of resources on servers and

i is the interest of node (number of resources desired by apeer). We extract from the networks some graphs. The firstgraph is the profile graph (called also reference graph). Thenodes of the reference graph are all nodes of the network andan edge is created between two nodes if the similarity be-tween the interest of these two nodes is larger than a definedthreshold. The similarity between two nodes is calculatedusing the Jaccard’s index. The reference graph represents thereal connections between similar nodes in the network. So,the extracted communities in this graph are the real existingcommunities of the network. The aim is to look for whichcommunication graph giving communities closer to thecommunities given by the reference graph. In this purpose,we extract three different communication graphs from thenetwork: simple, weighted and completed communicationgraph. For each graph (reference graph and communicationgraphs), we apply a community detection algorithm to detectcommunities and we extract some community properties.Using these properties, we do microscopic and macroscopiccomparison between communities of the reference graph andcommunities of the communication graphs.

A. Communication graphs

The communication graph is the one representing therelationship between nodes communicating more. The edgesof this graph have as signification, at least, one communi-cation between two nodes. We mean by communication anexchange of resources (peer v1 ask v2 for a resource and v2

replays to v1 by sending the asked resource).1) Simple communication graph: Let SCG = (Vs, Es)

be an unweighted undirected graph representing the simplecommunication graph. Vs represents the node set of thenetwork. Es is the edge set of the simple graph. If two nodesin the network communicate, we make an edge betweenthese two nodes.

2) Weighted communication graph: Let WCG =(Vw, Ew) be a weighted undirected graph representing theweighted communication graph. The weighted graph issimilar to the simple graph with the difference that we countthe number of communications done between nodes.

3) Completed communication graph: Let CCG =(Vc, Ec) be an unweighted undirected graph representingthe completed communication graph. The completed graphis the simple graph for which we add some hidden links.

2010 International Conference on Advances in Social Networks Analysis and Mining

978-0-7695-4138-9/10 $26.00 © 2010 IEEE

DOI 10.1109/ASONAM.2010.37

393

2010 International Conference on Advances in Social Networks Analysis and Mining

978-0-7695-4138-9/10 $26.00 © 2010 IEEE

DOI 10.1109/ASONAM.2010.37

393

2010 International Conference on Advances in Social Networks Analysis and Mining

978-0-7695-4138-9/10 $26.00 © 2010 IEEE

DOI 10.1109/ASONAM.2010.37

393

(a) (b)

(c) (d)

Figure 1. Community structure comparison. (a) the clustering coefficient ofthe reference graph and the three communication graphs (simple, weightedand completed). (b) community comparison using the normalized mutualinformation (NMI). (c) density of the formed communities. (d) quality ofthe communities, measured by the modularity.

The hidden links are added between nodes having a closeinterest.

III. SIMULATIONS AND COMPARISONS

We use NS2 (Network Simulation 2) to generate allgraphs and to detect communities. We use the fast algorithmof Newman [4] to detect communities. A measure of thepartition called the modularity is done. The modularityis a measure that qualifies the partitions. Once with thecommunities, we extract some properties to analyze them.The extracted community properties are: number of resultingcommunities, size of the communities (number of nodes ineach community), modularity of the partition, density of thecommunities (proportion of edges in each community) andthe clustering coefficient of the emerged communities. Theseproperties can be ranked in two classes: microscopic andmacroscopic properties.

A. Macroscopic comparison

The macroscopic analysis is done by looking first atthe clustering coefficient. Figure 1(a) shows the cluster-ing coefficient of the four graphs. The largest coefficientclustering is the reference graph one, meaning that socialbehavior exists and appears in networks. Figure 1(a) showsalso that the closest graph to the referential is the com-pleted communication graph. The hidden edges added tothe completed graph make it closer to the reference one. Wealso remark that the weighted graph is the farthest to thereferential. In the weighted graph, edges with low weight areremoved, thus affecting the number of triangles and so theclustering coefficient will be lower. The second macroscopiccomparison is done by using a measure to compare twopartitions. Authors in [3] define a measure to compare twopartitions. The defined measure is the normalized mutualinformation (nmi). We use the nmi measure to compare the

communities of the reference graph with the communitiesof the three communication graphs. Figure 1(b) shows thatboth, simple and completed graphs, are the closest to thereferential.

B. Microscopic comparison

We take the two properties, community size and thedensity, to do this comparison. Figure 1(c) shows the averagedensity of the graphs. The density of the reference graph isthe largest one (see Figure 1(c), red bloc). The referencegraph is constructed by looking the interest of nodes. So,the formed community of this graph will have the maximumnumber of possible edges relating the nodes in communities(all real connections between nodes having closer interest).We remark that the completed communication graph isthe one that have the density closer than the density ofthe reference graph. Completed communication graph isconstructed by adding some hidden edges. It’s why it theclosest one. Figure 1(c) shows also that no communicationgraph has the same density like the reference graph. Thatmeans, the three communication graphs don’t discover allthe real interest relations between nodes.

IV. CONCLUSION

In this paper we have showed the emergence of commu-nities of interest in communication networks. Three differ-ent communication graphs are studied and compared withthe referential (the graph representing the real connectionsof interest in the network). The results showed that thecommunication graphs have the community structures. Thatmeans, groups of peers in networks share the same interestand, usually, communicate together. The results showedalso that both the simple and the completed graphs arecloser to the real one, owing to the fact that the com-munities detected in these graphs are very closer to thereals. However, the microscopic comparison showed thatno communication graph discover all the real connectionsexisting in the network. As perspective, we intend to applyour study to an existing protocol network and analyze itsemerged community structures.

REFERENCES

[1] F. Bloch and B. Dutta. Communication networks with endoge-nous link strength. Games & Eco. Behav., 66(1):39–56, 2009.

[2] V. Carchiolo, M. Malgeri, G. Mangioni, and V. Nicosia.Emerging structures of p2p networks induced by social rela-tionships. Comput. Commun., 31(3):620–628, 2008.

[3] L. I. Kuncheva and S. T. Hadjitodorov. Using diversity incluster ensembles. In IEEE inter. conf. on systems, man &cybernetics (SMC), pages 1214–1219, 2004.

[4] M. E. J. Newman. Fast algorithm for detecting communitystructure in networks. Physical Review E, 69:066133, 2004.

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