Overlapping Communities Explain CorePeriphery Organization of Networks

Overlapping CommunitiesExplain CorePeripheryOrganization of NetworksPiyush Goel303/co/11COE - 21Communities in networksNetworks represent system of interacting objects.Nodes denote objectsEdges denote interactionsNodes organize into communities group of nodes that share common property, role or function.Communities often overlap nodes belong to multiple communities at once.

Protein Protein Interaction network

Structural to Functional communitiesStructural CommunitiesSets of nodes with many connections among members of the set and few connections to the rest of the network.

Functional CommunitiesBased on function or role of communitys members.Biological modules in PPI networks, social groups in social networks.Community detectionBuild a bridge between network structure and function.Identify communities based on network structure such thatStructurally identified communities Functional communitiesCommunity detectionFacebook friendship network of a user

Define communities as tilesEdge density in overlaps is higher

Define communities as tilesEdge density in overlaps is higherCore-periphery structure network is composed ofDensely connected coreSparsely connected periphery

Define communities as tiles

Community detectionGiven a model, we generate a network

Given a networkFind the best modelDetect communities

The Affiliation Graph ModelGenerative model for networks

AGM: Generative Process

AGM: Generative Process

AGM: FlexibilityAGM can express a variety of community structures:Non overlappingOverlappingNestedCommunity detection with AGMGiven a graph G(V,E), we detect communities by finding a model B and parameters {pc} which maximizes the likelihood that B generates G.

Accuracy of detected communities

Accuracy of detected communitiesConclusionThe AGM models structural communities as tiles rather that densely connected sets of nodes.Regions of the network where communities overlap have higher density of edges than non-overlapping regions.This explains the core-periphery structure exhibited by networks where nodes that belong to multiple communities reside in the core.