workflow hybrid-network-community-analysis template: contextualise (LinLog layout) -> visualise (node-link) -> abstract (identify clusters) -> loop(generate-knowledge (select community) -> define-unit (aggregate) -> contextualise (hybrid layout) -> visualise (NodeTrix) -> abstract (identify patterns) -> abstract (test membership) -> assess) -> generate-knowledge (synthesis) description: "Social network analysts explore globally-sparse, locally-dense networks by iteratively aggregating identified communities into adjacency matrices within a node-link diagram. The hybrid NodeTrix representation enables simultaneous inspection of global structure (bridging actors, component topology) and community-level detail (collaboration patterns, missing edges, cliques). Interactive manipulation — moving actors in/out of matrices, merging, splitting, adjusting link thickness — supports progressive community identification, central actor detection, and role/position analysis." # ============================================================================ # INPUT # ============================================================================ artifact D_actors : entities origin: given internal structure: elementary embedment: set features: - id: f_name value structure: atomic value type: categorical description: "Actor name (e.g., researcher name)" - id: f_citations value structure: atomic value type: numeric description: "Numerical attribute (e.g., citation count)" - id: f_affiliation value structure: atomic value type: categorical description: "Categorical attribute (e.g., institution, country)" description: "Actors (vertices) in the social network: researchers in the InfoVis coauthorship network with associated attributes (name, citation count, affiliation); 1,104 actors total, 122 in the largest connected component" artifact D_relationships : entities origin: given internal structure: elementary embedment: set features: - id: f_source value structure: atomic value type: reference description: "Source actor of the relationship" - id: f_target value structure: atomic value type: reference description: "Target actor of the relationship" - id: f_strength value structure: atomic value type: numeric description: "Relationship strength (e.g., number of co-authored papers)" description: "Relationships (edges) in the social network: co-authorship links between researchers with collaboration strength; 1,787 total edges; network is globally sparse but locally dense (small-world properties: high clustering coefficient, short average path length)" # ============================================================================ # STEP 1: INITIAL LAYOUT # ============================================================================ transform T_compute_layout : intent: contextualise manner: "apply LinLog energy-based layout algorithm to the full network; this layout gives prominence to clusters by placing densely connected subgraphs as compact spatial groups while separating loosely connected regions; produces 2D positions for all actors" input: D_actors, D_relationships output: A_network actor: machine description: "Compute cluster-emphasising node-link layout for the full network using LinLog energy model" artifact A_network : arrangement(D_actors) context: "LinLog energy-based layout" principle: "2D positions computed by LinLog algorithm; densely connected communities appear as tight spatial groups; sparse inter-community connections span larger distances; hub nodes positioned between communities they bridge" description: "Initial node-link arrangement emphasising cluster structure through energy-based spatial grouping" transform T_vis_nodelink : intent: visualise manner: "render actors as nodes with configurable shape, size, and colour; render relationships as links with configurable thickness and colour; map citation count to node colour; map collaboration strength to link opacity or thickness; support pan, zoom, lasso selection, and drag-and-drop interactions" input: A_network output: V_network actor: machine description: "Generate the initial node-link diagram with interactive manipulation support" artifact V_network : visualisation(A_network) layout: "2D canvas with LinLog-positioned nodes and straight-line edges" form: "filled circles for actors; straight lines for relationships; labels on nodes" encoding: "node position: LinLog layout; node colour: citation count; link thickness: collaboration strength; link opacity: configurable via slider" description: "Initial node-link diagram showing the network with cluster-emphasising layout, configurable visual mappings, and interactive manipulation support (lasso, drag-and-drop)" # ============================================================================ # STEP 2: GLOBAL STRUCTURE INSPECTION # ============================================================================ transform T_identify_clusters : intent: abstract manner: "inspect node-link diagram for spatial clusters (tight groups of actors indicating communities); identify hub nodes with many visible links radiating outward; note bridges between clusters (actors connecting separate groups); identify isolated peripheral actors; form initial hypotheses about community boundaries" input: V_network output: P_community_findings actor: human description: "Inspect the node-link diagram to identify community clusters, hub nodes, and bridging actors at the global level" artifact P_community_findings : pattern(D_actors) representation form: "identified communities, structural roles, and collaboration patterns" description: "Accumulated findings about network structure: identified communities with collaboration patterns, central/bridging actors, role categorisations, and overall topology; initially contains global structure observations from the node-link overview; grows across iterations as communities are aggregated and inspected" # ============================================================================ # STEP 3: ITERATIVE HYBRID CONSTRUCTION AND EXPLORATION # ============================================================================ # Accumulated community aggregations (initially empty) artifact D_communities : entities origin: given internal structure: group/cluster embedment: set features: - id: f_member_actors value structure: set value type: reference description: "Set of actors comprising this community" - id: f_internal_density value structure: atomic value type: numeric description: "Edge density within the community" - id: f_community_label value structure: atomic value type: categorical description: "Community label (e.g., 'Berkeley', 'PARC')" description: "Aggregated community entities represented as matrices in the hybrid NodeTrix visualisation; internal connections shown as filled matrix cells, external connections as links from axis items; initially empty; grows as communities are progressively aggregated" loop L_exploration: purpose: "Iteratively aggregate communities into matrices, inspect intra-community collaboration patterns and inter-community bridges, manipulate actor membership to test boundaries, and build up a comprehensive understanding of communities, central actors, and connection roles" until: "Analyst has identified all significant communities, characterised their collaboration patterns (cross, block, intermediate), identified all bridging actors, and constructed a readable hybrid layout suitable for communication" body: # ======================================================================== # Step 3a: Select community for aggregation # ======================================================================== transform T_select_community : intent: generate-knowledge manner: "identify a dense cluster in the current visualisation that would benefit from matrix representation; lasso-select the actors comprising this community; or drag a single node onto another to begin a 2x2 matrix; or drag a node into an existing matrix to extend it; or decide to merge two adjacent matrices, split a heterogeneous matrix, or rearrange node positions; selection guided by spatial proximity in layout and by accumulated findings" input: V_network, P_community_findings output: S_aggregation_spec actor: human description: "Select actors to aggregate into a matrix community, or decide on a structural manipulation (merge, split, rearrange) based on identified cluster structure and exploration progress" artifact S_aggregation_spec : specification representation form: "manipulation directive: actor set for new aggregation, merge/split instruction, or rearrangement parameters" description: "Aggregation or manipulation specification: set of actors to combine into a new matrix, instruction to merge or split existing matrices, or parameters for rearrangement" # ======================================================================== # Step 3b: Aggregate into matrix # ======================================================================== transform T_aggregate : intent: define-unit manner: "execute the specified manipulation: create an aggregated node for newly selected actors (internal relationships become matrix cells, external relationships become links from axis items); or merge existing matrices into one larger matrix; or split one matrix into separate sub-matrices; animate the transition to maintain mental model; compute aggregated attributes" input: D_actors, D_relationships, D_communities, S_aggregation_spec output: D_communities_r actor: machine description: "Execute the structural manipulation: aggregate selected actors into a community matrix, merge or split existing matrices, updating the accumulated community set" artifact D_communities_r : entities internal structure: group/cluster embedment: set features: - id: f_member_actors value structure: set value type: reference description: "Set of actors comprising this community" - id: f_internal_density value structure: atomic value type: numeric description: "Edge density within the community" - id: f_community_label value structure: atomic value type: categorical description: "Community label" description: "Updated set of aggregated communities reflecting the latest aggregation, merge, or split operation" # ======================================================================== # Step 3c: Arrange and visualise hybrid # ======================================================================== transform T_arrange_hybrid : intent: contextualise manner: "position matrices at aggregated node locations; display internal relationships as filled cells (colour-coded by collaboration strength); display external relationships as links from matrix axis items to outside nodes or other matrices; maintain node-link layout for non-aggregated actors; axis labels show individual actor names; matrix size adjustable via slider" input: D_communities_r, D_actors, D_relationships output: A_hybrid actor: machine description: "Arrange the hybrid NodeTrix representation with matrices embedded in the node-link layout" artifact A_hybrid : arrangement(D_actors, D_communities_r) context: "hybrid node-link + matrix layout" principle: "aggregated communities as matrices positioned at their LinLog centroid; non-aggregated actors as standard nodes; inter-community links as edges from matrix axis items; intra- community links as matrix cells; link thickness adjustable for overview vs. detail" description: "Hybrid NodeTrix arrangement combining node-link global structure with matrix community detail" transform T_vis_hybrid : intent: visualise manner: "render matrices with cells coloured by collaboration strength; axis labels showing actor names with citation colour; render inter-community links with adjustable thickness (slider from thin individual links to thick merged bands); support drag-and-drop of actors in/out of matrices, matrix merging, matrix splitting, row/column reordering, and geometric zoom on matrices via sliders" input: A_hybrid output: V_network_r actor: machine description: "Render the NodeTrix hybrid visualisation with full interactive manipulation support" artifact V_network_r : visualisation(A_hybrid) layout: "2D canvas: matrices positioned at community centroids; standard nodes at LinLog positions; links connecting matrices to external elements" form: "square matrices with coloured cells and labelled axes; circles for non-aggregated actors; lines/bands for inter- community links; animated transitions on aggregation" encoding: "matrix cell colour intensity: collaboration strength; axis label colour: citation count; link thickness: adjustable (thin = individual underlying links, thick = merged band approximating aggregated link); matrix background colour: aggregated community attribute; node size: configurable" description: "NodeTrix hybrid visualisation: matrices for communities within a node-link global structure, with interactive manipulation (drag-and-drop, merge, split, thickness slider, size slider, label toggle)" # ======================================================================== # Step 3d: Identify intra-community collaboration patterns # ======================================================================== transform T_identify_patterns : intent: abstract manner: "inspect matrix fill patterns to categorise collaboration structure: 'cross pattern' (single complete row/column in sparse matrix — one central actor collaborates with all, but others do not collaborate among themselves, indicating supervisor-student structure); 'block pattern' (near-clique — most cells filled, indicating tight mutual collaboration); 'intermediate pattern' (central actor plus partial block); identify missing edges within near-cliques; note community density and size" input: V_network_r, P_community_findings output: P_community_findings_r actor: human description: "Inspect matrix patterns to categorise community collaboration structures (cross, block, intermediate)" artifact P_community_findings_r : pattern(D_actors) representation form: "updated community and pattern descriptions" description: "Updated findings: identified collaboration patterns per community (cross = star topology indicating hierarchical group, block = clique indicating peer collaboration, intermediate = mixed); noted community densities and sizes; identified missing relationships within near-cliques" # ======================================================================== # Step 3e: Test community membership and identify bridges # ======================================================================== transform T_test_membership : intent: abstract manner: "drag actors in and out of matrices to test community boundaries: extract a suspected bridging actor and observe if the matrix becomes disconnected (confirming articulation point role); add peripheral actors to matrices to test if they belong to the community; inspect inter-community links to identify which actors bridge communities; adjust link thickness slider to switch between 'how are communities linked?' (thick bands) and 'who links them?' (thin individual links)" input: V_network_r, P_community_findings_r output: P_community_findings_r2 actor: human description: "Test community boundaries and identify bridging actors through interactive manipulation and observation" artifact P_community_findings_r2 : pattern(D_actors) representation form: "further updated findings with bridge and role information" description: "Further refined findings: confirmed articulation points (actors whose removal disconnects a community), identified bridges between communities, validated or adjusted community boundaries, and characterised actor roles (supervisor, peer, bridge, peripheral)" # ======================================================================== # Step 3f: Assess exploration progress # ======================================================================== transform T_assess_exploration : intent: assess manner: "judge whether all significant communities have been aggregated and their patterns characterised; evaluate whether all bridging actors have been identified; determine if the current hybrid layout is sufficiently readable for communication; consider whether remaining non-aggregated clusters warrant matrix treatment or whether further merging/splitting would clarify the structure" input: P_community_findings_r2, V_network_r output: K_exploration_state actor: human description: "Assess whether all communities and central actors have been sufficiently characterised" artifact K_exploration_state : knowledge(P_community_findings_r2) representation form: "quality judgment" description: "Assessment of exploration progress: all communities identified and characterised, all bridges found, and layout suitable for communication; or further aggregation, splitting, or manipulation needed for specific regions of the network" if K_exploration_state indicates sufficient characterisation: then: assign: D_communities := D_communities_r V_network := V_network_r P_community_findings := P_community_findings_r2 exit loop L_exploration else: assign: D_communities := D_communities_r V_network := V_network_r P_community_findings := P_community_findings_r2 end loop L_exploration # ============================================================================ # STEP 4: KNOWLEDGE SYNTHESIS AND PRESENTATION # ============================================================================ transform T_compose_presentation : intent: generate-knowledge manner: "compose a final NodeTrix layout optimised for communication: adjust matrix positions to minimise link crossings; reduce axis labels (via slider) for compactness in overview mode or keep them visible for detailed mode; choose appropriate colour mappings (axis colour = citations, cell intensity = collaboration strength); set link thickness for desired overview/detail balance; add community labels; produce the summary visualisation communicating global structure and community-level patterns simultaneously" input: P_community_findings, V_network output: K_network_understanding actor: human description: "Compose final summary visualisation and synthesise analytical findings about communities, central actors, and roles" artifact K_network_understanding : knowledge(P_community_findings) representation form: "analytical conclusions and summary visualisation" description: "Synthesised social network understanding: (1) identified communities with characterised collaboration patterns — Berkeley (block/clique pattern indicating tight mutual collaboration), Shneiderman et al. (cross pattern indicating supervisor-student structure), PARC (block pattern), Roth/CMU (intermediate pattern); (2) identified central and bridging actors (e.g., Ed Chi as articulation point in PARC); (3) characterised inter-community relationships (sparse bridges connecting dense communities, confirming small-world properties); (4) final NodeTrix summary visualisation simultaneously communicating global topology and community detail without the readability problems of either pure node-link (cluttered in dense regions) or pure matrix (no path following for global structure)"