• in-degree: how many directed edges (arcs)are incident on a node• out-degree: how may directed edgesoriginate at a node• Degree sequence: [4, 4, 3, 7, …]Node properties
Generated properties of node• Clustering coefﬁcient: how your neighborsconnected together• ego-density: density of the surrounding netUCINET: Network>Ego-networks>egonet basic measures
• Directed or undirected• Weight, ranking, ...• Type, negative or positive, ...• Assigned-properties depending oncalculating network itself, e.g., betweennessEdge properties
Network Properties• Degree distribution: Frequency of degreesequences• Size: number of nodes (n)• Density: real relations divided by the maximumpossible relations• Diameter: the length of the longest path• Average degree of separation:Average length of allpossible shorted pathUCINET: Network>Cohesion>Density
• DegreeHow many resource do you have?• ClosenessHow far apart are you from others?• BetweennessHow important are you for bridgingsub-communities?• CentralizationHow balanced are actors’ centrality?CentralityIndividuallevelGloballevel
• DensityHow does the network tied together?• Separation, DiameterHow far apart are you and your friends?• Cluster CoefﬁcientHow do your neighbors be connected?IndividuallevelGloballevel
Visualization through analysis process1. Take a look2. Analyze and ﬁnd signiﬁcant features such as sub-components or special positions3. Draw the network according to the result ofanalysis4. Color by the node features (e.g., sex, position, ...)and create hypothesis5. Verify the hypothesis
• Ego-network Analysis--• Partial Network Analysis- One, two or three steps network two steps network- Boundary or sub-cluster of network• Whole Network Analysis- /Motif-Levels of network analysis
• Data is recorded with a clear natural-occurringboundary and nodes in a boundary form a ﬁniteset.• What should be a possible boundary?‣ A ﬁxed location or room, speciﬁed time or day, a ﬁnite contacttracing, a formal group in an organization, a family.‣ The boundary is known or decided ﬁrstly, a priori, to be anetwork.Policy of recording data
• No sampling and tend to include all of the actorsin some population(s).• Because network methods focus on relationsamong actors, actors cannot be sampledindependently to be included as observations.Policy of recording data (2)
• positivity A Priorimetaphysics-• -• --Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
• Closed Complete- ﬁniteset-• Singularity-• Consistency-Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
• Different relation sampling policy will causedifferent results—Threshold effects on networkproperties• ThresholdThreshold• Threshold 0ConnectednessBetweenness• Threshold BetweennessDegree Betweenness• facebook10Application
• Full network data is necessary to properly deﬁne and measuremany of the structural concepts of network analysis (e.g.between-ness), however, very expensive.• Snowball methods begin with a focal actor or set of actors untilno new actors are identiﬁed, or until we decide to stop.- Useful to track down “special” population such as business contact networks, communityelites, deviant sub-cultures, avid stamp collectors, and kinship networks.- The snowball method may tend to overstate the "connectedness" and "solidarity" ofpopulations of actors.- There is no guaranteed way of ﬁnding all of the connected individuals in the population.- How to select the ﬁrst node (initial problem of sampling)?- Incomplete problem of the snowball methods can be solved by use of multiple initial nodes.Methods of sampling ties
X Crossed-edgesX Uninformed-edgelengthX Overlappednodes and edges
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